Question

Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).

Answer 1

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)`