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Question

Find the coordinates of the points of trisection of the line segment joining (4,1) and (2,3).

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Solution

Let A(4,1) and B(2,3) be the points of trisection of P and Q

so AP=PQ=QB

For P:

m1:m2=AP:PB=1:2

(x1,y1)=(4,1)

and (x2,y2)=(2,3)

x=m1x2+m2x1m1+m2

x=1×2+2×41+2=2+83=63=2

y=m1y2+m2y1m1+m2=1×3+2×11+2=323=53

P=(2,53)

For Q:

m1:m2=AQ:QB=2:1

(x1,y1)=(4,1) and

(x2,y2)=(2,3)

x=m1x2+m2x1m1+m2

x=2×2+1×41+2=4+43=03=0

y=m1y2+m2y1m1+m2=2×3+1×11+2=613=73

Q=(0,73)

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