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A line intersects the y–axis and x–axis at points P and Q respectively. If (2, –5) is the mid–point of PQ, then co–ordinates of P and Q are respectively.

Answer:

P lies on y–axis so co–ordinates of P are (0, y).

Similaraly, co–ordinates of Q lies on x–axis = Q(x, 0)

Mid–point of PQ is

M\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\mathrm{M}(2,-5), \text { which is given }\\ \Rightarrow M\left(\frac{0+x}{2}, \frac{y+0}{2}\right)=\mathrm{M}(2,-5)\\ \Rightarrow\left(\frac{x}{2}, \frac{y}{2}\right)=\mathrm{M}(2,-5)

Comparing both side, we get

\frac{x}{2} = 2\text{ and }\frac{y}{2} = -5

⇒ x = 4 and y = –10

Hence, the co–ordinates of P(0, –10) and Q(4, 0).

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