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.

Answer 1

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).