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Find the vertices of a triangle midpoint of whose  sides are  (3,1), (5,6)and ( - 3,2)?

Asked by hemanttkumarr 9th October 2017, 7:11 PM
Answered by Expert
Answer:
begin mathsize 16px style Given space that space mid minus points space of space whose space sides space are space left parenthesis 3 comma 1 right parenthesis comma space left parenthesis 5 comma 6 right parenthesis space and space left parenthesis negative 3 comma space 2 right parenthesis
Let space straight A comma space straight B comma space straight C space are space the space vertices space of space the space increment ABC space and space left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis comma space space left parenthesis straight x subscript 2 comma space straight y subscript 2 right parenthesis space and space left parenthesis straight x subscript 3 comma space straight y subscript 3 right parenthesis
fraction numerator straight x subscript 2 space plus space straight x subscript 3 over denominator 2 end fraction space equals 3 space and space fraction numerator straight y subscript 2 space plus space straight y subscript 3 over denominator 2 end fraction equals 1
straight x subscript 2 space plus space straight x subscript 3 space equals space 6 space and space straight y subscript 2 space plus space straight y subscript 3 space equals space 2............ left parenthesis 1 right parenthesis
Similarly comma
fraction numerator straight x subscript 3 space plus space straight x subscript 1 over denominator 2 end fraction equals 5 space and space fraction numerator straight y subscript 3 space plus space straight y subscript 1 over denominator 2 end fraction equals 6
straight x subscript 3 space plus space straight x subscript 1 space equals space 10 space and space straight y subscript 3 space plus space straight y subscript 1 space equals space 12......... left parenthesis 2 right parenthesis
fraction numerator straight x subscript 1 space plus space straight x subscript 2 over denominator 2 end fraction equals negative 3 space and space fraction numerator straight y subscript 1 space plus space straight y subscript 2 over denominator 2 end fraction equals 2
straight x subscript 1 space plus space straight x subscript 2 space equals space minus 6 space and space straight y subscript 1 space plus space straight y subscript 2 space equals space 4............. left parenthesis 3 right parenthesis
Adding space three space equations space
2 open parentheses straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 close parentheses space equals space 6 plus 10 minus 3 space space space
straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 space equals space 6.5............. left parenthesis 4 right parenthesis
and space
2 open parentheses straight y subscript 1 plus straight y subscript 2 plus straight y subscript 3 close parentheses equals 2 plus 12 plus 4
straight y subscript 1 plus straight y subscript 2 plus straight y subscript 3 space equals space 9............. left parenthesis 5 right parenthesis
Consider comma
straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 space equals space 6.5 space given space that space straight x subscript 1 space plus space straight x subscript 2 space equals space minus 6
minus 6 space plus straight x subscript 3 space equals space 6.5
space straight x subscript 3 space equals 12.5
Similarly space you space can space find space the space other space coordinates space of space vertices space for space straight x space and space straight y.

end style
Answered by Expert 18th December 2017, 10:56 AM
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