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Two sides of 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 vertices of this rhombus?

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(-3,-8)

answer is D.

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Detailed Solution

Point intersection of the two sides is (1,2)
Diagonal passing through (1,2) and (-1,-2) is
Question Image

As diagonal of rhombus are perpendicular to each other and also passing through (-1,-2)
Its equation by

Putting (-1,-2) in equation

Equation of other diagonal is 2y+x+5=0
Solving this equation with 2x-y-5=0
We get the vertex point

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