Question

find the coordinates of the point of trisection of the line segment joining a(-5,4) and b(7,-8)

Answer 1

Trisection Ratio is 1:2 or 2:1
Let P be the point of Trisection.
Therefore, by Section Formula taking ratio as 1:2,
P(x, y) = { [1(7) + 2(-5)]/(1 + 2), [1(-8) + 2(4)]/(1 + 2) }
P(x, y) = (-1, 0)
llly, by Section Formula taking ratio as 2:1,
P(x, y) = { [2(7) + 1(-5)]/(2 + 1), [2(-8) + 1(4)]/(2 + 1) }
P(x, y) = (3, -4)