question_answer

If P\[\left( \frac{a}{3},4 \right)\]is the mid-point of the line segment joining the points Q \[(6-5),\]and R\[(-2,3)\]then the value of a is

A)  \[-11\]                          

B)  \[-12\]

C)  15                               

D)  16

Correct Answer: B

Solution :

Mid-point of QR is P\[\left( \frac{-\,\,6-2}{2},\frac{5+3}{2} \right)\]or P \[(-\,\,4,4)\] But mid-point P\[\left( \frac{a}{3},4 \right)\]is given \[\left( \frac{a}{3},4 \right)\cong (-\,\,4,4)\] On comparing the coordinates, we get \[\frac{a}{3}=-\,\,4\] \[\therefore \]                  \[a=-\,\,12\]