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Question
The slope of aline joining P(6,k) and Q(1 - 3k, 3) is `1/2` Find
(i) k.
(ii) mid-point of PQ, using the value of 'k' found in (i).
Solution
(i) Slope of PQ = `(3 - k)/(1 - 3k - 6)`
`=> 1/2 = (3 - k)/(-3k - 5)`
`=>` -3k - 5 = 2(3 - k)
`=>` -3k - 5 = 6 - 2k
`=>` k = -11
(ii) Substituting in P and Q, we get
P(6, k) = P(6, 11) and Q(1 - 3k,3) = Q(34, 3)
Mid point of PQ = `((6 + 34)/2, (-11 + 3)/2) = (40/2, (-8)/2) = (20, -4)`
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