Thread: Point to line distance equation

The problem says, find the equation that expresses the distance from P(7,7) to a line that crosses the origin and has slope m, as a function of m. Or d(m) = ?

I have found several equations in rectangular and polar coordinates and what the graph should look like, but have been unable to express d as a function of m. I would appreciate some help.

If a line has slope m, then any line perpendicular to it has slope -1/m. In particular, a line through (7, 7) perpendicular to a line with slope m must be given by y= -(1/m)(x- 7)+ 7.

Of course, a line through the origin with slope m has equation y= mx. So you must solve y= mx= -(1/m)(x- 7)+ 7 for x. Find the y value from y= mx, and then find the distance from that (x, y) to (7, 7).

Originally Posted by BERMES39

The problem says, find the equation that expresses the distance from P(7,7) to a line that crosses the origin and has slope m, as a function of m. Or d(m) = ?

Given the point and the line then the distance from is

The line in your question is so the distance is