Theory question 104
Coordinate GeometryA straight line passes through the point P(−1, 3). Another line which passes through Q(−4, 4) intersects the first line at a point R(k, 5), where k is constant. If ∠PRQ = 90° find the values of K.
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Model answer
Gradient of PR = (5 − 3)/(k + 1) = 2/(k + 1)
Gradient of QR = (5 − 4)/(k + 4) = 1/(k + 4)
Perpendicular: product = −1, so 2 = −(k + 1)(k + 4)
k2 + 5k + 6 = 0, (k + 2)(k + 3) = 0
k = −2 or k = −3
Explanation
Lines at right angles have gradients whose product is −1.