# Thread: Finding point on a line closest to another line

1. ## Finding point on a line closest to another line

 Find the point on the line x + y − 2 = 0 that is closest to the point (-2, 5)

2. ## Re: Finding point on a line closest to another line

What you want is the intersection of the line perpendicular to the given line which passes through the given point. Can you proceed?

3. ## Re: Finding point on a line closest to another line

So a line orthogonal to x + y - 2 = 0?

4. ## Re: Finding point on a line closest to another line

Originally Posted by biggerleaffan
So a line orthogonal to x + y - 2 = 0?
Note that $\displaystyle x-y+7=0$ is a line through $\displaystyle (-2,5)$ and perpendicular to the given line.

Where do they intersect?

5. ## Re: Finding point on a line closest to another line

Originally Posted by Plato
Note that $\displaystyle x-y+7=0$ is a line through $\displaystyle (-2,5)$ and perpendicular to the given line.

Where do they intersect?
-5/2, 9/2.

Is this then the answer to my original question?

6. ## Re: Finding point on a line closest to another line

Originally Posted by biggerleaffan
-5/2, 9/2.
Is this then the answer to my original question?
I don't know if that is correct. I will not do the algebra.

But by definition: the distance from a point to a line is the length of the line segment from the point to the line.

7. ## Re: Finding point on a line closest to another line

Originally Posted by Plato
I don't know if that is correct. I will not do the algebra.

But by definition: the distance from a point to a line is the length of the line segment from the point to the line.
There are many "line segments from the point to the line".

By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line.

8. ## Re: Finding point on a line closest to another line

Originally Posted by HallsofIvy
There are many "line segments from the point to the line".

By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line.
RIGHT! I have no idea where my "perpendicular" went to. Clearly a typo. Thank you.