First, find the slope of AD = [ 7 - 2 ] 5 5
_______ = ----- = - ___
[ 1 - 8] -7 7
The slope of a perpendicular line to this = 7
__
5
So....using D and this slope we have that
y = (7/5) ( x - 8) + 2 multiply through by 5
5y = 7 (x - 8) + 10
5y = 7x - 56 + 10
5y = 7x - 46
-7x + 5y = -46 multiply through by -1
7x - 5y = 46 (1)
This line will intersect AB
The equation of AB is y = 7
Sub y = 7 into (1) and we have that
7x - 5(7) = 46
7x - 35 = 46 add 35 to both sides
7x = 81 divide both sides by 7
x = 81/7 = x coordinate of E
So
E = (81/7, 7)