Question

# The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

A

P=(4,83)Q=(10,9)

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B

P=(8,9)Q=(4,23)

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C

P=(2,203)Q=(0,163)

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D

P=(4,9)Q=(5,45)

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Solution

## The correct option is C P=(2,203)Q=(0,163) Let, P and Q be point of Trisection. AP = PQ = QB and AP:PB = 1:2 The part of the line from (4, 8) to P is one third of AB. Coordinates by section formula (x,y)=(mx2+nx1m+n,my2+ny1m+n) ∴ x-coordinate of P =4×2−2×13=8−23=2 y-coordinate of P =8×2+4×13=16+43=203 Therefore coordinates of point P are (2,203) Also since AP = PQ = QB, AQ:QB = 2:1 The part of the line from (4,8) to Q is two third the length of AB. Again, by section formula we have, x-coordinate of Q =4×1−2×23=0 y-coordinate of Q =8×1+4×23=163 Therefore coordinates of point Q are (0,163)

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