Theorem 1.10: Given a line whose equation is
and a point whose coordinates are
the coordinates of the foot of the point in the line are
Proof: By Theorem 1.6, the coordinates of the point of intersection of the perpendicular line through (x1, y1) with the line y = mx + b are
and
where
by Theorem 1.9,
and
We substitute these in and get
by Theorem 1.6. Multiply top and bottom by m to clear denominators
and
again by Theorem 1.6. Again, multiply top and bottom by m to clear denominators
