{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":45278,"title":"Orthogonal lines","description":"Check whether two given lines are orthogonal or not.\r\n\r\nTwo lines are orthogonal if they create a right angle at their intersections.\r\n\r\n* p=[x1 y1; x2 y2]   \r\n* q=[x3 y3; x4 y4]\r\n\r\nhere (x1,y1) and (x2,y2) form a line.","description_html":"\u003cp\u003eCheck whether two given lines are orthogonal or not.\u003c/p\u003e\u003cp\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/p\u003e\u003cul\u003e\u003cli\u003ep=[x1 y1; x2 y2]\u003c/li\u003e\u003cli\u003eq=[x3 y3; x4 y4]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/p\u003e","function_template":"function tf = ortho_line(p,q)","test_suite":"%%\r\np=[7,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,3;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[2,2;5,5];\r\nq=[0,-2;-2,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-26T06:07:02.000Z","updated_at":"2026-03-05T16:46:12.000Z","published_at":"2020-01-26T06:07:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether two given lines are orthogonal or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[x1 y1; x2 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[x3 y3; x4 y4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":450,"title":"What is the distance from point P(x,y) to the line Ax + By + C = 0?","description":"Given a point, P(x,y), find the distance from this point to a linear line.\r\n\r\nINPUTS: x, y, A, B, C\r\n\r\nOUTPUTS: d, the distance which of course should always be positive.\r\n    \r\n  EX:\r\n  \u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n  \u003e\u003ed = normalLen(x,y,A,B,C)\r\n  d = 1.4142\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/p\u003e\u003cp\u003eINPUTS: x, y, A, B, C\u003c/p\u003e\u003cp\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eEX:\r\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n\u003e\u003ed = normalLen(x,y,A,B,C)\r\nd = 1.4142\r\n\u003c/pre\u003e","function_template":"function d = normalLen(x,y,A,B,C)\r\n  d = x+y+[A,B,C]\r\nend","test_suite":"%% test 1\r\nx=2; y=2; A=2; B=2; C=-4;\r\ny_correct = 1.4142;\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c=1e-4)\r\n%% test 2\r\nx=3; y=4; A=3; B=4; C=5;\r\ny_correct = 6;\r\nassert(normalLen(x,y,A,B,C)-y_correct==0)\r\n%% test 3\r\nx=4; y=5; A=3; B=4; C=5;\r\ny_correct = 7.4;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c1e-1)\r\n%% test 4\r\nx=0;y=12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n%% test 5\r\nx=0;y=-12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":"2013-01-26T00:45:07.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-03-05T04:51:25.000Z","updated_at":"2026-03-13T05:04:32.000Z","published_at":"2012-03-06T06:29:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eINPUTS: x, y, A, B, C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[EX:\\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\\n\u003e\u003ed = normalLen(x,y,A,B,C)\\nd = 1.4142]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":451,"title":"Is this matrix orthogonal?","description":"Given a square matrix, a, determine whether it is orthogonal.\r\nINPUT: a, a n x n matrix\r\nOUTPUT: true or false","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a square matrix, a, determine whether it is orthogonal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eINPUT: a, a n x n matrix\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOUTPUT: true or false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isOrthogonal(x)\r\n  y = x;\r\nend","test_suite":"%% test one\r\nx = orth(randn(3));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test two\r\nx = orth(randn(4));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test three\r\nx = orth(randn(5));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test four\r\nx=sqrt([3,1;1,1]);\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test five\r\nx = magic(6);\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test six\r\nx = randn(2)+1;\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%%Test cases added by Dyuman Joshi, 2-8-23\r\n%% test seven\r\nx = [1 0; 0 0];\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test eight\r\nx = eye(3);\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test nine\r\nx = -eye(6);\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test ten\r\nx = [1 0 0 0; 0 0 0 1; 0 0 1 0; 0 1 0 0]; \r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":1103,"edited_by":223089,"edited_at":"2023-08-02T08:02:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":"2023-08-02T08:02:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-05T05:06:16.000Z","updated_at":"2026-03-24T05:24:36.000Z","published_at":"2012-03-06T04:36:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a square matrix, a, determine whether it is orthogonal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eINPUT: a, a n x n matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOUTPUT: true or 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form a line.\u003c/p\u003e","function_template":"function tf = ortho_line(p,q)","test_suite":"%%\r\np=[7,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,3;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[2,2;5,5];\r\nq=[0,-2;-2,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-26T06:07:02.000Z","updated_at":"2026-03-05T16:46:12.000Z","published_at":"2020-01-26T06:07:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether two given lines are orthogonal or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[x1 y1; x2 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[x3 y3; x4 y4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":450,"title":"What is the distance from point P(x,y) to the line Ax + By + C = 0?","description":"Given a point, P(x,y), find the distance from this point to a linear line.\r\n\r\nINPUTS: x, y, A, B, C\r\n\r\nOUTPUTS: d, the distance which of course should always be positive.\r\n    \r\n  EX:\r\n  \u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n  \u003e\u003ed = normalLen(x,y,A,B,C)\r\n  d = 1.4142\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/p\u003e\u003cp\u003eINPUTS: x, y, A, B, C\u003c/p\u003e\u003cp\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eEX:\r\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n\u003e\u003ed = normalLen(x,y,A,B,C)\r\nd = 1.4142\r\n\u003c/pre\u003e","function_template":"function d = normalLen(x,y,A,B,C)\r\n  d = x+y+[A,B,C]\r\nend","test_suite":"%% test 1\r\nx=2; y=2; A=2; B=2; C=-4;\r\ny_correct = 1.4142;\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c=1e-4)\r\n%% test 2\r\nx=3; y=4; A=3; B=4; C=5;\r\ny_correct = 6;\r\nassert(normalLen(x,y,A,B,C)-y_correct==0)\r\n%% test 3\r\nx=4; y=5; A=3; B=4; C=5;\r\ny_correct = 7.4;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c1e-1)\r\n%% test 4\r\nx=0;y=12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n%% test 5\r\nx=0;y=-12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":"2013-01-26T00:45:07.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-03-05T04:51:25.000Z","updated_at":"2026-03-13T05:04:32.000Z","published_at":"2012-03-06T06:29:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eINPUTS: x, y, A, B, C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[EX:\\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\\n\u003e\u003ed = normalLen(x,y,A,B,C)\\nd = 1.4142]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":451,"title":"Is this matrix orthogonal?","description":"Given a square matrix, a, determine whether it is orthogonal.\r\nINPUT: a, a n x n matrix\r\nOUTPUT: true or false","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a square matrix, a, determine whether it is orthogonal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eINPUT: a, a n x n matrix\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOUTPUT: true or false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = isOrthogonal(x)\r\n  y = x;\r\nend","test_suite":"%% test one\r\nx = orth(randn(3));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test two\r\nx = orth(randn(4));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test three\r\nx = orth(randn(5));\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test four\r\nx=sqrt([3,1;1,1]);\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test five\r\nx = magic(6);\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test six\r\nx = randn(2)+1;\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%%Test cases added by Dyuman Joshi, 2-8-23\r\n%% test seven\r\nx = [1 0; 0 0];\r\ny_correct = false;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test eight\r\nx = eye(3);\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test nine\r\nx = -eye(6);\r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))\r\n\r\n%% test ten\r\nx = [1 0 0 0; 0 0 0 1; 0 0 1 0; 0 1 0 0]; \r\ny_correct = true;\r\nassert(isequal(isOrthogonal(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":1103,"edited_by":223089,"edited_at":"2023-08-02T08:02:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":"2023-08-02T08:02:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-05T05:06:16.000Z","updated_at":"2026-03-24T05:24:36.000Z","published_at":"2012-03-06T04:36:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a square matrix, a, determine whether it is orthogonal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eINPUT: a, a n x n matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOUTPUT: true or 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