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. |
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