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Question

If P(9a2,b) divides the line segment joining A(3a+1,2) and B(8a,5) in the ratio 3:1. Find the value of a and b.

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Solution

Point P divides AB in the ratio 3:1

By using section formula

x=mx2+nx1m+n and y=my2+ny1m+n

3(8a)+3a+14=9a2

9a=9

a=1

And,

3(5)+1(2)4=b

4b=13

b=134

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