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Question

Find the coordinates of the points that divide the join of A(−4, 0) and B(0, 6) in three equal parts.


Solution

Let P and Q be the points of trisection of AB.
Then, P divides AB in the ratio 1:2.
So, the coordinates of P are
x =mx2+nx1m+n, y = my2+ny1m+nx= 1×0 + 2×-41+2, y =1×6+2×01+2x= -83, y = 63x = -83, y = 2Therefore, coordinates of P are -83, 2.
Also Q divides AB in the ratio 2:1
So the coordinates of Q are
x =mx2+nx1m+n, y = my2+ny1m+nx= 2×0 + 1×-42+1, y =2×6+1×02+1x= -43, y = 123x = -43, y = 4Therefore, coordinates of Q are -43, 4.
Hence, the points are -83, 2 and -43, 4.

Mathematics
RS Aggarwal (2015)
Standard X

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