Thread: The shortest distance from Point A to the line...

I really need some help with finding out the Shortest distance from
Point A (2,0) to the line X-Y+4=0.
It would be nice if someone could
explain the steps to answering this question.
(You can leave out the actual distance formula since I'm well aware of how that works)

Originally Posted by DPXJube

I really need some help with finding out the Shortest distance from
Point A (2,0) to the line X-Y+4=0.
It would be nice if someone could
explain the steps to answering this question.
(You can leave out the actual distance formula since I'm well aware of how that works)

Find a normal vector from the line running through the point.

dwsmith is exactly right. The shortest distance to a geometric object is always along the line perpendicular to that object.

Here, the line is x- y+ 4= 0 which is the same as y= x+ 4. What is the slope of that line?

What is the slope of a line perpendicular to that line? What is the equation of a line with this new slope and passing through (2, 0)?

Where do those two lines intersect?

What is the distance from the point of intersection to (2, 0)?