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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.
Solution
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
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