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Question

Two sides of a rhombus are along the lines x-y+1=0 and 7x-y-5=0. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus?


A

(3,9)

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B

(3,8)

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C

(13,83)

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D

(103,73)

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Solution

The correct option is C

(13,83)


As the given lines xy+1=0 and 7xy5=0 are not parallel, therefore they represent the adjacent sides of the rhombus.
On solving xy+1=0 and 7xy5=0, we get x=1 and y=2 Thus, one of the vertex is A(1,2).

Let the coordinate of point C be (x, y).
Then, 1=x+12 and 2=y+22
x+1=2 and y=42
x=3
and y=6
Hence, coordinates of C=(3,6)
Note that, vertices B and D will satisfy x-y+1=0 and 7x-y-5=0, respectively
Since option (c) satisfies 7x - y - 5=0, therefore coordinate of vertex D is (13,83)


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