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Question

The slope of a line joining P(6,k) and Q(13k,3) is 12. Find midpoint of PQ

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Solution

Let P(6,k)=(x1,y1) and Q(13k,3)=(x2,y2)
Slope of PQ=y2y1x2x1
3k13k6=12
62k=53k
11=k
k=11
Hence, P(6,11) and Q(1(3×11),3)(34,3)
Midpoint of PQ(x1+x22,y1+y22)(6+342,11+32)(20,4)

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