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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)
Solution
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
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