Question

If the diagonals of the quadrilateral formed by the lines

px + qy + r = 0, p'x + q'y + r = 0, px + qy + r' = 0,p'x + q'y + r' = 0 are at right angles, then-

• A. p² + r² = p'² + r'²
• B. pp' + qq' = 0
• C. p² + q² = p'² + q'²
• D. q² + r² = q'² + r'²

Answer 1

Answer: (C)

p² + q² = p'² + q'²

Answer 2

The quadrilateral is obviously a parallelogram and if the diagonals are at right angles, it must be a rhombus. Hence the distance between the pairs of opposite sides must be the same.

(i.e.) $\left| \frac { \mathrm { r } - \mathrm { r } ^ { \prime } } { \sqrt { \mathrm { p } ^ { 2 } + \mathrm { q } ^ { 2 } } } \right| = \left| - \frac { \mathrm { r } - \mathrm { r } ^ { \prime } } { \sqrt { \mathrm { p } ^ { \prime 2 } + \mathrm { q } ^ { \prime 2 } } } \right|$

Ž p² + q² =