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 :
Let the coordinates of P and Q (0, y) and (x, 0), respectively. |
So, the mid-point of P (0, y) and Q (x, 0) is \[M\left( \frac{0+x}{2},\,\frac{y+0}{2} \right)\] |
. [ \[\because\] mid-point of a line segment having points \[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},\,{{y}_{2}} \right)\] |
\[\left. =\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\,\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \right]\] |
But it is given that, mid-point of \[PQ\] is (2,-5). |
\[\therefore \,\,\,\,\,2=\frac{x+0}{2}\] and \[-5=\frac{y+0}{2}\] |
\[\Rightarrow \,\,\,4=x\] and \[-10=y\] |
\[\Rightarrow \,\,\,x=4\] and \[y=-10\] |
So, the coordinates of P and Q are (0, - 10) and (4, 0). |
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