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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 =4×22×13=823=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 =4×12×23=0

y-coordinate of Q =8×1+4×23=163
Therefore coordinates of point Q are (0,163)


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