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Question
Find the coordinates of the points of trisection of the line segment joining the points A(−5, 6) and B(4, −3)
Solution
Let P and Q be the point of trisection
so that AP = PB = QB
The point P = `((x_2 + 2x_1)/3, (y_2 + 2y_1)/3)`
= `((4 + 2(-5))/3, (-3 + 2(6))/3)`
= `((4 - 10)/3, (-3 + 12)/3)`
= `((-6)/3, 9/3)`
= (−2, 3)
The point Q = `((2x_2 + x_1)/3, (2y_2 + y_1)/3)`
= `((2(4) + (-5))/3, (2(-3) + (6))/3)`
= `((8 - 5)/3, (-6 + 6)/3)`
= `(3/3, 0/3)`
= (1, 0)
The point P is (−2, 3), and point Q is (1, 0)
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