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Question
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Solution
Let the co-ordinates of point Q be (10, y).
PQ = 10
PQ2 = 100
(10 - 2)2 + (y + 3)2 = 100
64 + y2 + 9 + 6y = 100
y2 + 6y - 27 = 0
y2 + 9y - 3y - 27 = 0
y(y + 9) - 3(y + 9) = 0
(y + 9) (y - 3) = 0
y = -9, 3
Thus, the required co-ordinates of point Q are (10, -9) and (10, 3).
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