Posted by **math...** on Monday, June 6, 2011 at 4:25am.

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

- geometry (maths) -
**Reiny**, Monday, June 6, 2011 at 7:12am
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

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