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Question
The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:
- k.
- 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
`=>` –3k + 2k = 6 + 5
`=>` –k = 11
`=>` k = –11
ii. Substituting k in P and Q, we get
P(6, k) = (6, –11)
And Q(1 – 3k, 3) = (1 – 3(–11), 3)
= (1 + 33, 3)
= (34, 3)
∴ Midpoint of PQ = `((6 + 34)/2, (-11 + 3)/2)`
= `(40/2, (-8)/2)`
= (20, −4)
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