10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

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: (NCERT EXEMPLAR)

A) \[-4\]

B) \[-12\]

C) \[12\]

D) \[-6\]

Correct Answer: B

Solution :

[b] Given that, \[P\left( \frac{a}{3},4 \right)\] is the mid-point of the line segment joining the point \[Q(-6,5)\] and \[R(-2,3).\]

\[\therefore \]Mid-point of

\[QR=P\left( \frac{-6-2}{2},\frac{5+3}{2} \right)=P\left( -4,4 \right)\]

But mid-point is given as \[P\left( \frac{a}{3},4 \right)\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\left( \frac{a}{3},4 \right)=(-4,4)\]

On comparing the coordinates, we get, \[\frac{a}{3}=-4\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=-12\]