Question

Points P(a, −4), Q(−2, b) and R(0, 2) are collinear. If Q lies between P and R, such that PR = 2QR, calculate the values of a and b.

Answer 1

Given, PR = 2QR

Now, Q lies between P and R, so, PR = PQ + QR

∴ PQ + QR = 2QR

`=>` PQ = QR

`=>` Q is the mid-point of PR.

∴ `(-2, b) = ((a + 0)/2, (-4 + 2)/2)`

`(-2, b) = (a/2, -1)`

`=>` a = −4 and b = –1