Calculating the shortest distance of any given coordinate point to the line y=3x+2

I am trying to figure out how I can calculate the shortest distance of any give cordinate point to the line y=3x+2

I have tried using the following code to do this:

x = 0:0.1:100;

y = 3*x + 2;

plot(x,y);

grid on

pt = [5,0]

a = x - y;

b = pt - y;

d = norm(cross(a,b)) / norm(a);

distance = point_to_line(pt,x,y);

This gives me the following error:

pt =

5 0

Matrix dimensions must agree.

Error in eka (line 10)

b = pt - y;

Any help is highly appreciated with this.

Answer 1

[John D'Errico]

You have done a fair amount.

Surely you could just look online.

https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line

On there, you would find a very simple formula to compute the distance from a point (x0,y0), to a line. There the line is assumed to be of the form: a*x + b*y + c == 0. So your line has the form 3*x - y + 2 == 0.

For example, what is the distance to the line from the point (5,6)?

x0 = 5;
y0 = 6;
a = 3;
b = -1;
c = 2;
D = abs(a*x0+ b*y0 + c)/sqrt(a^2 + b^2)

D = 3.4785

[Esa Kesti]

Thanks for your help John, I am complete Noob with everything related to Matlab, trying to learn this from online is not the easiest way. People like you make learning this much more understandable.

Took me a while to understand that you solved my issue and I do appreciate it.

Answer 2

[Image Analyst]

See my attached point-to-line demo.