Question

y=x The point F is the foot of the perpendicular from the point (1, 9) to the line y=x. Find the coordinates of F.​

Answer 1

Answer: (5,5)

Explanation:

The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is
`y=-x+10`.

Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.

If x=5, then y=5 as well.

So, F has coordinates (5,5).