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Question
Show that A (3, –2) is a point of trisection of the line segment joining the points (2, 1) and (5, −8). Also, find the co-ordinates of the other point of trisection.
Solution
Let A and B be the points of trisection of the line segment joining the points P (2, 1) and Q (5, −8).
So, PA = AB = BQ
We have PA : AQ = 1 : 2
Co-ordinates of the point A are
`((1 xx 5 + 2 xx 2)/(1 + 2),(1 xx (-8) + 2 xx 1)/(1 + 2))`
= `(9/3, (-6)/3)`
= (3, −2)
Hence, A (3, −2) is a point of trisection of PQ.
We have PB : BQ = 2 : 1
Co-ordinates of the point B are
`((2 xx 5 + 1 xx 2)/(2 + 1),(2 xx (-8) + 1 xx 1)/(2 + 1))`
`((10 + 2)/3, (-16 + 1)/3)`
= (4, −5)
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