Finding the intersect between 2 lines

Hello, very simple question, however, I have tried using multiple methods, such as polyxpoly() from the Mapping Toolbox to find the intersection between these 2 lines, but I cannot see what the issue is. I have just used a simulatneous equation (as shown in the code) to solve for the equation just to get an output as polyxpoly() wasn't returning anything. The y value seems correct, but the x value is widely incorrect.

Here is my code:

xrt = linspace((1/297.7), (1/446.1), 20000)

m11 = -197.7506;
x11 = 0.0031;
b11 = 20.8898;
line1=m11*(xrt-x11)+b11;
plot(xrt, line1, '-')

hold on;

m22 = -897.4321;
x22 = 0.0029'
b22 = 20.9819;
line2=m22*(xrt-x22)+b22;
plot(xrt, line2, '-')

x_intersect = (b22-b11)/(m11-m22) %find the x point
y_intersect = m11*x0+b11

plot(x_intersect,y_intersect,'r*')

The output values for x_intersect and y_intersect:

Any help would be greatly appreciated.

Thanks.

[Rik]

Actually your math is incorrect, as the y-value is not correct either:

xrt = linspace((1/297.7), (1/446.1), 20000);

m11 = -197.7506;
x11 = 0.0031;
b11 = 20.8898;
line1=@(xrt) m11*(xrt-x11)+b11;

m22 = -897.4321;
x22 = 0.0029';
b22 = 20.9819;
line2=@(xrt) m22*(xrt-x22)+b22;

x_intersect = (b22-b11)/(m11-m22) %find the x point

x_intersect = 1.3163e-04

y_intersect = line2(x_intersect)

y_intersect = 23.4663

plot(xrt, line1(xrt), '-')
hold on;
plot(xrt, line2(xrt), '-')
plot(x_intersect,y_intersect,'r*')

[Tb]

Ok, but how do I solve this? Thanks

Answer 1

[James Tursa]

If you want the intersection of two lines and you have the equations of the lines, just use backslash. E.g., if you have these equations:

y = m1*x + b1

y = m2*x + b2

Then your system is equivalently

y - m1*x = b1

y - m2*x = b2

or

[1 -m1;1 -m2]*[y;x] = [b1;b2]

So the intersection point is just

[1 -m1;1 -m2] \ [b1;b2]

You just need to plug in the appropriate m and b values for your two lines.

m1 = m11

b1 = m11*(-x11)+b11;

m2 = m22

b2 = m22*(-x22)+b22;

[Tb]

This worked out perfectly. Thank you.

Answer 2

[David Hill]

xrt = linspace((1/297.7), (1/446.1), 20000);
m11 = -197.7506;
x11 = 0.0031;
b11 = 20.8898;
line1=@(x)m11*(x-x11)+b11;
plot(xrt, line1(xrt), '-');
hold on;
m22 = -897.4321;
x22 = 0.0029;
b22 = 20.9819;
line2=@(x)m22*(x-x22)+b22;
plot(xrt, line2(xrt), '-');
A=[1,-m11;1,-m22];
b=[b11-m11*x11;b22-m22*x22];
c=A\b;
plot(c(2),c(1),'g*');