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 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
Answer This Question
Related Questions
 mathematics  ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, ...
 Geometry  Determine the vertices of rectangle ABCD, where AB = 2BC. a) ...
 Math (Geometry)  ABCD is a rectangle with AC=20 and AB=2BC. What is the area of...
 maths plse help me..  ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT...
 maths plse help me..  ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT...
 maths  ABCD is a rhombus and AB is produced to E and F such that AE=AB=BF. ...
 mathscircles  ABCD is a rectangle the line through C perpendicular to AC meets...
 Maths (Geometry)  P is a point in rectangle ABCD. The distance from P to the 4 ...
 QUADRILATERAL MATHS  ABCD is a quadrilateral with angle ABC a right angle. The ...
 maths  Given is a quadrilateral ABCD,diagonals AC and BDare such that AO=BO=CO=...
More Related Questions