question_answer

  A Line intersects the X-axis and Y-axis at the point P and Q respectively. If \[(3,-7)\] is the mid-point of PQ, then the coordinates of P and Q are:

A) \[(3,0),\,\,(0,-7)\]

B) x\[(-14,0),\,(0,6)\]

C) \[(-7,0),\,(0,3)\]

D) \[(6,0),\,(0,-14)\]

Correct Answer: D

Solution :

[d] Let \[P(a,0)\] and \[Q(0,b)\] be the points on X-axis and Y-axis and M be the mid-point of PQ,

\[\therefore \]Coordinater of M are

\[\left( \frac{a+0}{2},\frac{0+b}{2} \right)=\left( \frac{a}{2},\frac{b}{2} \right)\]

But, coordinates of M are \[(3,-7)\]

[Given]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\frac{a}{2}=3\]and \[\frac{b}{2}=-7\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,a=6\] and \[b=-14\]