question_answer

A Line intersects the Y-axis and X-axis at the points P and Q, respectively. If \[(2,-5)\] is the mid-point of PQ, then the coordinates of P and Q are, respectively: (NCERT EXEMPLAR)

A) \[(0,-5)\] and \[(2,0)\]

B) \[(0,10)\] and \[(-4,0)\]

C) \[(0,4)\] and \[(-10,0)\]

D) \[(0,-10)\] and \[(4,0)\]

Correct Answer: D

Solution :

[d] Let the coordinates of P and Q are \[(0,y)\]

and \[(x,0)\] respectively. So, the mid-point of \[P(0,y)\] and \[Q(x,0)\] is\[M\left( \frac{0+x}{2},\frac{y+0}{2} \right)\]

\[\left[ \begin{align}   & \text{Mid}-\text{point of a tine segment having end points} \\  & ({{x}_{1}},{{y}_{1}})\,\,and\,({{x}_{2}},{{y}_{2}})=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \\ \end{align} \right]\]But it is given that, mid-point PQ is \[(2,-5)\]

\[\therefore \,\,\,\,\,\,\,2=\frac{x+0}{2}\] and \[-5=\frac{y+0}{2}\,\,\Rightarrow \,\,x=4\] and \[y=-10\]

So, the coordinates of P and Q are \[(0,-10)\] and \[(4,0),\]respectively.