Given endpoints: A (3,4) and B (1,5)
x₁ = 3 x₂ = 1
y₁ = 4 y₂ = 5
First Division Point:1/3 of the segment
(x,y) = [ x₁ + ¹/₃ (x₂ - x₁), y₁ + ¹/₃ (y₂-y₁) ]
= [ 3 + ¹/₃ (1-3), 4 + ¹/₃ (5-4) ]
= [ 3 + ¹/₃ (-2), 4 + ¹/₃ (1) ]
= ( 3 - 2/3, 4 + 1/3)
= ( 2 ¹/3, 4¹/₃)
= (7/3, 13/3)
First division point is (7/3, 13/3)
Second Division point: 2/3 of the segment
(x,y) = [ 3 + ²/₃(1 - 3), 4 + ²/₃(5 - 4) ]
= [3 + ²/₃ (-2) , 4 + ²/₃ (1) ]
= [3 - 4/3, 4 + 2/3 ]
= ( 5/3, 14/3)
Second Division point is (5/3, 14/3).
The points (7/3, 13/3) and (5/3, 14/3) are the points of division when the given segment is divided into three equal part.
