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Question 9
The point P(5,-3) is one of the two points of trisection of line segment joining the points A(7,-2) and B(1,-5).

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Solution

True
Let P(5,-3) divides the line segment joining the points A(7,-2) and B(1,-5) in the ratio K:1 internally.
By section formula, the coordinate of point P will be
(k(1)+(1)(7)k+1,k(5)+1(2)k+1)i.e.,(k+7k+1,5k2k+1)Now,(5,3)=(k+7k+1,5k2k+1)k+7k+1=55k+5=k+74k=2k=12
So the point P divides the line segment AB in ratio 1:2.
Hence, point P in the point of trisection of AB.

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