Projecting a point into a line

How can I project a point (let's say (50,0)) to a line (y = 5.6x - 7.1)?

Thank you.

[Mark Sherstan]

Look at the answer here

[Donigo Fernando Sinaga]

How can I define a function y = 9.1*x -135.3396 in 'vector' variable? And how can I plot like that?

[Adam Danz]

If you look at the example in the link Mark provided, you'll see that the vector variable is actually a 2x2 matrix of the endpoint coordinates of the line.

Since you already have the slope, intercept, and (x,y) coordinates of another point, I suggest using the method proposed in the answer section.

Answer 1

[Adam Danz]

You need the equation of both perpendicular lines. You already have the equation for the first line. In your line y = 5.6x - 7.1 the slope is 5.6.

The slope of the second line will just be the perpendicular slope of your first line.

m = 5.6; 
b = -7.1; 
x = 50; 
y = 0; 
perpSlope = -1/m; 

To get the y intercept of the 2nd line you just need to solve for y=mx+b using your point (x,y)

yInt = -perpSlope * x + y;

Now you've got the two linear equations and you need to find out where they intersect. Here we find the x coordinate of the intersection. m and b are the slope and intercept of line 1, perSlope and yInt are the slope and intercept of line 2.

xIntersection = (yInt - b) / (m - perpSlope); 

To get the y coordinate of the intersection, we just plug the x coordinate into one of the equations.

yIntersection = perpSlope * xIntersection + yInt; 

Now we can plot it out to make sure it looks rights

figure
plot(x,y, 'rx')
hold on
plot(xIntersection, yIntersection, 'ro')
refline(m, b)
refline(perpSlope, yInt)
axis equal

[Donigo Fernando Sinaga]

Thank you very much, your answer really helps me. Thank you!