ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpendicular AC.

Answer 1

let AB = x
then BC = 2x
CE = 2(2x) = 4x

slope BE = 4x/(2x) = 2
slope AC = -x/(2x) , negative since it leans to the left
= -1/2

since 2 is the negative reciprocal of -1/2,
BE and AC are perpendicular.

or

place rectangle ABCD on the x-y grid with B at the origin.
A is (0,x)
B is (,0)
C is (2x, 0)
D is (2x, x)
E is (2x, 4x)

find slope BE and slope AC to show the same result