Question

Find the value(s) of k so that PQ will be parallel to RS. Given : P(5, −1), Q(6, 11), R(6, −4k) and S(7, k²)

Answer 1

Since, PQ || RS,

Slope of PQ = Slope of RS

Slope of PQ = `(11 + 1)/(6 - 5) = 12/1 = 12`

Slope of RS = `(k^2 + 4k)/(7 - 6) = k^2 + 4k`

∴ 12 = k² + 4k

k² + 4k – 12 = 0

(k + 6)(k – 2) = 0

k = –6 and k = 2