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)

Solution:

Let P(0, y) and Q(x, 0) be the coordinates.

Midpoint of PQ = (2, -5)

The midpoint of a line having coordinates (x1, y1) and (x2,y2) = ((x1+x2)/2, (y1+y2)/2)

=> (0+x)/2 = 2 and (y+0)/2 = -5

=> x = 4 and y = -10

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

Hence option d is the answer.

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