Question

If the coordinates of the points A, B, C, D, be $( a , b )$ $\left( a ^ { \prime } , b ^ { \prime } \right)$ $( - a , b )$ and $\left( a ^ { \prime } , - b ^ { \prime } \right)$ respectively, then the

equation of the line bisecting the line segments AB and CD is.

• A. $2 a ^ { \prime } y - 2 b x = a b - a ^ { \prime } b ^ { \prime }$
• B. $2 a y - 2 b ^ { \prime } x = a b - a ^ { \prime } b ^ { \prime }$
• C. $2 a y - 2 b ^ { \prime } x = a ^ { \prime } b - a b ^ { \prime }$
• D. None of these

Answer 1

Answer: (B)

$2 a y - 2 b ^ { \prime } x = a b - a ^ { \prime } b ^ { \prime }$

Answer 2

Mid point of $A B = E \left( \frac { a + a ^ { \prime } } { 2 } , \frac { b + b ^ { \prime } } { 2 } \right)$and mid point of $C D = F \left( \frac { a ^ { \prime } - a } { 2 } , \frac { b - b ^ { \prime } } { 2 } \right)$. Hence equation of line EF is

$= \frac { b - b ^ { \prime } - b - b ^ { \prime } } { a ^ { \prime } - a - a - a ^ { \prime } } \left( x - \frac { a + a ^ { \prime } } { 2 } \right)$

On simplification, we get $2 a y - 2 b ^ { \prime } x - = a b - a ^ { \prime } b ^ { \prime }$.