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

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).