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ICSE Class 10 Answered

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Asked by rdk_kulkarni | 07 Sep, 2020, 05:16: PM
answered-by-expert Expert Answer
Question: If a(-6, 0) and b(0, 6) are two points. Find the points of trisection of line segment AB.
Solution:
begin mathsize 14px style Let space straight P space and space straight Q space be space the space points space of space trisection. space
Then comma space AP space equals space PQ space equals space QB
Let space straight A left parenthesis negative 6 comma space 0 right parenthesis equals straight A left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis space and space straight B left parenthesis 0 comma space 6 right parenthesis equals straight B left parenthesis straight x subscript 2 comma space straight y subscript 2 right parenthesis
Now comma space straight P space divides space AB space in space the space ratio space 1 space colon space 2 space and space straight Q space divides space AB space in space the space ratio space 2 space colon space 1.
therefore space Coordinates space of space straight P equals open parentheses fraction numerator 1 cross times 0 plus 2 cross times left parenthesis negative 6 right parenthesis over denominator 1 plus 2 end fraction comma space fraction numerator 1 cross times 6 plus 2 cross times 0 over denominator 1 plus 2 end fraction close parentheses equals open parentheses fraction numerator negative 12 over denominator 3 end fraction comma space 6 over 3 close parentheses equals open parentheses negative 4 comma space 2 close parentheses
space space space space space Coordinates space of space straight Q equals open parentheses fraction numerator 2 cross times 0 plus 1 cross times left parenthesis negative 6 right parenthesis over denominator 2 plus 1 end fraction comma space fraction numerator 2 cross times 6 plus 1 cross times 0 right parenthesis over denominator 2 plus 1 end fraction close parentheses equals open parentheses fraction numerator negative 6 over denominator 3 end fraction comma space 12 over 3 close parentheses equals open parentheses negative 2 comma space 4 close parentheses
Hence comma space the space two space points space of space trisection space are space straight P left parenthesis negative 4 comma space 2 right parenthesis space and space straight Q left parenthesis negative 2 comma space 4 right parenthesis. end style
Answered by Renu Varma | 08 Sep, 2020, 11:09: AM

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