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Question
Find the co-ordinates of the points of tri-section of the line joining the points (–3, 0) and (6, 6).
Solution
Let P and Q be the point of trisection of the line segment joining the points A (–3, 0) and B (6, 6).
So, AP = PQ = QB
We have AP : PB = 1 : 2
Co-ordinates of the point P are
`((1 xx 6 + 2 xx (-3))/(1 + 2),(1 xx 6 + 2 xx 0)/(1 + 2))`
= `((6 - 6)/3, 6/3)`
= (0, 2)
We have AQ : QB = 2 : 1
Co-ordinates of the point Q are
`((2 xx 6 + 1 xx (-3))/(2 + 1),(2 xx 6 + 1 xx 0)/(2 + 1))`
= `((9)/3, 12/3)`
= (3, 4)
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