Coordinate Geometry-6

Find the points of trisection of the line segment joining the points (2, -1)and (5, 2).

Solution: --A(2, -1)--------------C------------------D------------------B(5, 2)--

Let C and D be the points which divide the line segment AB into three equal parts

i.e. AC = CD = DB

C and D are the points of trisection of AB

AC : CB = 1 : 2

AD : DB = 2 : 1

Let C be (x₁, y₁) and D be (x₂, y₂)

Then x₁ = [1(5) + 2(2)] / (1+ 2) = 9/3 = 3

y₁ = [1(2) + 2(-1)] / (1 + 2) = 0/3 = 0

Therefore, C = (x₁, y₁) = (3, 0)

x₂ = [2(5) + 1(2)]/(2 + 1) = 12/3 = 4

y₂ = [2(2) + 1(-1)] / (2 + 1) = 3/3 = 1

Therefore, D = (x₂, y₂) = (4, 1)