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?

x + y = -1

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x – y = -1

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x + y = 1

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None of these

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Solution

The correct option is A x + y = -1

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.

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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?

The correct option is A x + y = -1 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 ⇒ x+y= -1.

The correct option is A x + y = -1

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.