{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":57770,"title":"Number of images formed due to two inclined mirrors and their coordinates","description":"There are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. Final output should contain a vector of coordinates including the original object coordinate.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 249px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 124.5px; transform-origin: 407px 124.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. Final output should contain a vector of coordinates including the original object coordinate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 156px; 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 78px; text-align: left; transform-origin: 384px 78px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"170\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [N,y] = images(x,theta)\r\n  \r\nend","test_suite":"%%\r\nx = 2;\r\ntheta = pi;\r\nN_correct = 1;\r\ny_correct = [2 -2;0 0];\r\n[N,y] = images(x,theta)\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n\r\n%%\r\nx = 20;\r\ntheta = pi/4;\r\nN_correct = 7;\r\ny_correct =   [20    14     0   -14   -20   -14     0    14;\r\n                0    14    20    14     0   -14   -20   -14]\r\n\r\n[N,y] = images(x,theta)\r\n    \r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%% \r\nx = 1.1\r\ntheta = pi/2;\r\nN_correct = 3;\r\ny_correct =   [1.1000         0   -1.0000         0;\r\n                    0    1.0000         0   -1.0000];\r\n[N,y] = images(x,theta)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%%\r\nx = -10;\r\ntheta = 2*pi;\r\nN_correct = 0;\r\ny_correct = [-10;0];\r\n[N,y] = images(x,theta)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%%\r\nx = 20;\r\ntheta = 0;\r\nN_correct = Inf;\r\n[N,y] = images(x,theta);\r\n\r\nassert(isequal(N,N_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1809490,"edited_by":1809490,"edited_at":"2023-03-12T09:24:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2023-03-12T09:24:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-12T08:45:13.000Z","updated_at":"2023-03-12T09:24:24.000Z","published_at":"2023-03-12T09:10:51.000Z","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\u003eThere are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. 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of images formed due to two inclined mirrors and their coordinates","description":"There are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. Final output should contain a vector of coordinates including the original object coordinate.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 249px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 124.5px; transform-origin: 407px 124.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. Final output should contain a vector of coordinates including the original object coordinate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 156px; 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 78px; text-align: left; transform-origin: 384px 78px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"170\" height=\"156\" style=\"vertical-align: top;width: 170px;height: 156px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [N,y] = images(x,theta)\r\n  \r\nend","test_suite":"%%\r\nx = 2;\r\ntheta = pi;\r\nN_correct = 1;\r\ny_correct = [2 -2;0 0];\r\n[N,y] = images(x,theta)\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n\r\n%%\r\nx = 20;\r\ntheta = pi/4;\r\nN_correct = 7;\r\ny_correct =   [20    14     0   -14   -20   -14     0    14;\r\n                0    14    20    14     0   -14   -20   -14]\r\n\r\n[N,y] = images(x,theta)\r\n    \r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%% \r\nx = 1.1\r\ntheta = pi/2;\r\nN_correct = 3;\r\ny_correct =   [1.1000         0   -1.0000         0;\r\n                    0    1.0000         0   -1.0000];\r\n[N,y] = images(x,theta)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%%\r\nx = -10;\r\ntheta = 2*pi;\r\nN_correct = 0;\r\ny_correct = [-10;0];\r\n[N,y] = images(x,theta)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(N,N_correct))\r\n\r\n%%\r\nx = 20;\r\ntheta = 0;\r\nN_correct = Inf;\r\n[N,y] = images(x,theta);\r\n\r\nassert(isequal(N,N_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1809490,"edited_by":1809490,"edited_at":"2023-03-12T09:24:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2023-03-12T09:24:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-12T08:45:13.000Z","updated_at":"2023-03-12T09:24:24.000Z","published_at":"2023-03-12T09:10:51.000Z","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\u003eThere are two mirrors with angle theta between them and there is an object on x axis. Determine the number of images formed and the cordinates of the images when coordinate of the object on x axis is given. The coordinates will be given as x = 2 or x = 3 etc. Round the coordinates to the nearest integers. 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