If the quadrilateral formed by the lines ax+bc+c=0. a'x+b'y+c=0, ax+by+c'=0, a'x+b'y+c'=0 has perpendicular diagonal, then

Options

A. `b^(2) + c^(2) = b^(2) + c^(2)`
B. `c^(2) + a^(2) = c^(2) +a^(2)`
C. `a^(2) + b^(2) =a^(2) + b^(2)`
D. none of these

Answer

C

Explanation

Since the diagonal are perpendicular, so the given quadrilateral is a rhombus.
`therefore ` Distance between two pairs of parallel sides are equal
`rArr |(c'-c)/(sqrt(a^(2) +b^(2)))|=|(c'-c)/(sqrt(a^(2)+b^(2)))|rArr a^(2) + b^(2) = a^(2) + b^(2)`