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CBSE Class 10 Answered

The mid-point of the line AB as shown in the diagram is (-3, 5). Find the coordinates of A and B.
Asked by Topperlearning User | 26 Sep, 2017, 10:44: AM
answered-by-expert Expert Answer

begin mathsize 12px style Since comma space point space straight A thin space lies space on space the space straight x minus axis comma space coordinates space of space straight A equals left parenthesis straight x comma space 0 right parenthesis And comma space point space straight B thin space lies space on space the space straight y minus axis comma space coordinates space of space straight B equals left parenthesis 0 comma space straight y right parenthesis straight C left parenthesis negative 3 comma space 5 right parenthesis space is space the space mid minus point space of space AB. Now comma space by space mid minus point space formula comma space mid minus point space of space the space join space of space left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis space and space left parenthesis straight x subscript 2 comma space straight y subscript 2 right parenthesis space is space given space by open parentheses fraction numerator straight x subscript 1 plus straight x subscript 2 over denominator 2 end fraction comma space fraction numerator straight y subscript 1 plus straight y subscript 2 over denominator 2 end fraction close parentheses therefore space Mid minus point space of space AB equals space open parentheses fraction numerator straight x plus 0 over denominator 2 end fraction comma space fraction numerator 0 plus straight y over denominator 2 end fraction close parentheses therefore left parenthesis negative 3 comma space 5 right parenthesis equals open parentheses straight x over 2 comma space straight y over 2 close parentheses therefore minus 3 equals straight x over 2 space and space 5 equals straight y over 2 therefore space straight x equals negative 6 space and space straight y equals 10 Hence comma space the space coordinates space of space straight A space are space left parenthesis negative 6 comma space 0 right parenthesis space and space the space coordinates space of space straight B space are space left parenthesis 0 comma space 10 right parenthesis. end style

Answered by | 26 Sep, 2017, 12:44: PM

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