what are the points which divides the given line segment into 3 equal parts
Answers
points of trisection
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( 2x₁ + x₂)/3 , ( 2y₁ + y₂)/3 & ( x₁ + 2x₂)/3 , ( y₁ + 2y₂)/3 are the points which divides the given line segment into 3 equal parts
Step-by-step explanation:
Let say line Segment AB
A = (x₁ , y₁)
B = (x₂ , y₂)
Point C & D which divides the given line segment into 3 equal parts
=> AC = CD = DB
=> AC + CD + DB = AB
=> AC = CD = DB = AB/3
AC : CB = 1 : 2
AD : DB = 2 : 1
C = ( 1 * x₂ + 2*x₁)/(1 + 2) , ( 1 * y₂ + 2*y₁)/(1 + 2)
= ( 2x₁ + x₂)/3 , ( 2y₁ + y₂)/3
D = ( 2 * x₂ +1*x₁)/(2 + 1) , ( 2 * y₂ + 1*y₁)/(2 + 1)
= ( x₁ + 2x₂)/3 , ( y₁ + 2y₂)/3
( 2x₁ + x₂)/3 , ( 2y₁ + y₂)/3 & ( x₁ + 2x₂)/3 , ( y₁ + 2y₂)/3 are the points which divides the given line segment into 3 equal parts
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