15. The vertices of A DEF are D (0,0), E (0,7), and F (6,3).

Find the coordinates of the orthocenter of A DEF.

Orthocenter of a triangle with one vertex at the origin D (0,0), E (0,7), F (6,3)

The orthocenter is the meet of the altitudes.

DE is the line x=0. That's the y axis. The altitude is the perpendicular through F (6,3), so is the horizontal line y=3.

DF is the line

6y=3x

y = (1/2) x

Perpendicular through E (0,7) is

y - 7 = (-2) (x - 0)

y = - 2x + 7

That's the other altitude. Intersecting with y=3

3 = - 2x + 7

-4 = - 2x

x = 2

y = 3

Answer: orthocenter is (2,3)