# geometry (maths)

posted by .

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) -

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

## Similar Questions

1. ### Geometry

Can I get help starting this exercise:- Let triangle ABC be such that AB is not congruent to AC. Let D be the point of intersection of the bisector of angle A and the perpendicular bisector of side BC. Let E, F, and G be the feet of …
2. ### mathematics

ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpindicular AC
3. ### maths --plse help me..

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT 1) ar(EGB) = 1/6 ar(ABCD) 2)ar(EFC) = 1/2 ar(EBF) 3) ar(EBG) = ar(EFC) …
4. ### maths --plse help me..

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT 1) ar(EGB) = 1/6 ar(ABCD) 2)ar(EFC) = 1/2 ar(EBF) 3) ar(EBG) = ar(EFC) …
5. ### maths-circles

ABCD is a rectangle the line through C perpendicular to AC meets AB produced at X and AD produce at Y . Prove that DBXY are concyclic
6. ### Math (Geometry)

ABCD is a rectangle with AC=20 and AB=2BC. What is the area of rectangle ABCD?
7. ### Maths (Geometry)

P is a point in rectangle ABCD. The distance from P to the 4 vertices of the rectangle are 7,15,24 and N in some order. If N is an integer, determine the value of N.
8. ### maths

ABCD is a rhombus and AB is produced to E and F such that AE=AB=BF. Prove that ED and FC are perpendicular to each other.
9. ### Geometry

Determine the vertices of rectangle ABCD, where AB = 2BC. a) rectangle ABCD A) (0,0) B) (8,2) C (_,_) D (_,_) So far I just found the midpoint of A and B and got (4,1) but i don't know what to do after that. THe slope is 1/4, so i …