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Question

If P and Q are the points of trisection of the line joining A(2, -2) and B(-7, 4) such that P is nearer to A, then the coordinates of P and Q are:

A
P(0, -1), Q(-4, 2)
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B
P(-1, 0), Q(-4, 2)
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C
P(-1, 0), Q(4, -2)
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D
P(1, 0), Q(-4, -2)
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Solution

The correct option is B P(-1, 0), Q(-4, 2)
Given:P and Q are the points of trisection of the line joining A(2, -2) and B(-7, 4) such that P is nearer to A.
Let the coordinates of P and Q be P(x1,y1) and Q(x2,y2).

Point P is near to A.

P(x1,y1) divides AB in the ratio 1 : 2, while Q(x2,y2) divides AB in the ratio 2 : 1.
section formula;

P(x,y)=m1x2+m2x1m1+m2,m1y2+m2y1m1+m2
Thus, by section formula,
P(x1,y1)=(7+4)3,(44)3=(1,0)
Q(x2,y2)=(14+2)3,(82)3=(4,2)

Hence, coordinates of point P is (1,0) and point Q is (4,2).



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