If the quadrilateral formed by the lines ax + by + c = 0, a'x + b'y + c' = 0, ax + by + c' = 0,a'x + b'y + c = 0 have perpendicular diagonals, 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, the given quadrilteral is a rhombus. So, the distances between two pairs of parallel sides are equal. Hence,
`|(c'-c)/(sqrt(a^(2)+b^(2)))| = |(c'-c)/(sqrt(a'^(2)+b'^(2)))|`
`"or " a^(2) +b^(2) = a'^(2) + b'^(2)`