Find the coordinates of points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).

Asked by Topperlearning User | 26th Sep, 2017, 02:13: PM

Expert Answer:

begin mathsize 12px 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 2 comma space minus 2 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 negative 7 comma space 4 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 left parenthesis negative 7 right parenthesis plus 2 cross times 2 over denominator 1 plus 2 end fraction comma space fraction numerator 1 cross times 4 plus 2 cross times left parenthesis negative 2 right parenthesis over denominator 1 plus 2 end fraction close parentheses equals open parentheses fraction numerator negative 7 plus 4 over denominator 3 end fraction comma space fraction numerator 4 minus 4 over denominator 3 end fraction close parentheses equals open parentheses negative 1 comma space 0 close parentheses
space space space space space Coordinates space of space straight Q equals open parentheses fraction numerator 2 cross times left parenthesis negative 7 right parenthesis plus 1 cross times 2 over denominator 2 plus 1 end fraction comma space fraction numerator 2 cross times 4 plus 1 cross times left parenthesis negative 2 right parenthesis over denominator 2 plus 1 end fraction close parentheses equals open parentheses fraction numerator negative 14 plus 2 over denominator 3 end fraction comma space fraction numerator 8 minus 2 over denominator 3 end fraction close parentheses equals open parentheses negative 4 comma space 2 close parentheses
Hence comma space the space two space points space of space trisection space are space straight P left parenthesis negative 1 comma space 0 right parenthesis space and space straight Q left parenthesis negative 4 comma space 2 right parenthesis. end style

Answered by  | 26th Sep, 2017, 04:13: PM

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