geometry (maths)
posted by math... .
ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpendicular AC.

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 xy 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