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Question
Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).
Solution
Given: AP = PQ = BQ
∴ `(AP)/(BP) = 1/2`
and `(AQ)/(BQ) = 2/1`
Coordinate of P = `(m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2)`
= `(1 xx 4 + 2 xx 5)/(1 + 2), (1 xx 5 + 2 xx 3)/(1 + 2)`
= `(14/3, 11/3)`
Coordinate of Q = `(2 xx 4 + 1 xx 5)/(1 + 2), (2 xx 5 + 1 xx 3)/(1 + 2)`
= `(13/3, 13/3)`
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