A straight line passes through the point P(-1, 3). Another line which passes through Q(-4, 4) intersects the first line at the point R(k, 5), where k is a constant. If (<PRQ = 90°), find the values of k.
Explanation
(< PRQ = 90°)
Gradient of PR (times) Gradient of QR = -1.
(frac{5 – 3}{k + 1} times frac{5 – 4}{k + 4} = -1)
(frac{2}{(k + 1)(k + 4)} = -1)
(-2 = k^{2} + 5k + 4 implies k^{2} + 5k + 4 + 2 = 0)
(k^{2} + 5k + 6 = 0)
(k^{2} + 3k + 2k + 6 = 0)
(k(k + 3) + 2(k + 3) = 0 implies (k + 3)(k + 2) = 0)
(implies text{k = -2 or -3)