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Question

Find the co-ordinates of the points of trisection of the segment joining the points A(-7,4) and B(2,-2).

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

The correct options are
B (-1,0)
C (-4,2)
Let P and Q be the points of trisection of the line segment joining the points A and B.


Point P and point Q divide the line segment AB into 3 parts.
AP = PQ = QB ........(i)

APPB=APPQ+QB=APAP+AP=1AP2APAPPB=12
Point P divides segment AB in the ratio 1 : 2.

Co-ordinate of point by section formula (x, y)=(mx2+nx1m+n, my2+ny1m+n)
P(x,y)=(1×2+2×(7)1+2,1×(2)+2×41+2)P(x,y)=(123,63)=(4,2)

Point Q divides segment AB in the ratio 2 : 1.
Co-ordinate of point Q(x,y)=(2×2+1×(7)2+1,2×(2)+1×42+1)Q(x,y)=(33,03)=(1,0)

Co-ordinates of the points of trisection are (1,0) & (4,2).

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