ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the

Question

ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x y plane. The equation of the straight line AD is x + y =1. What is the equation of BC? (CAT 2000)

Options:

A . x + y = -1

B . x – y = -1

C . x + y = 1

D . None of these

Answer: Option A
:
A

Slope of line AD= -1

Hence, eqn of BC which passes through (0,-1) and (-1,0) and is parallel to x+y=1 is

(y-0)=-1(x+1)

Y=-x-1 $\Rightarrow$ x+y= -1. Option (a)

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