Question

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 find the coordinates of P and Q.

Answer 1

Suppose the line intersects the y-axis at P(0, y) and the x-axis at Q(x, 0)

It is given that (2, –5) is the mid-point of PQ

Using mid-point formula, we have

`((x+0)/2 , (0+y)/2) = (2, -5)`

`=> (x/2,y/2) = (2, -5)`

`=> x/2 = 2 and y/2 = -5`

`=> x = 4, y = - 10`

Thus, the coordinates of P and Q are (0, −10) and (4, 0), respectively.