Shean12idn
Answered

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the segment joining A (3,4) and B (1,5) is divided into three equal parts. Find the points of division

Sagot :

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.