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CBSE Class 11-science Answered

Find the coordinates of incentre of triangle formed by lines y-15=0,12y-5x=0,4y+3x=0.
Asked by lovemaan5500 | 08 Oct, 2018, 05:19: PM
answered-by-expert Expert Answer
begin mathsize 16px style First space draw space the space line space straight y minus 15 equals 0 minus negative negative negative left parenthesis 1 right parenthesis space comma 12 straight y minus 5 straight x equals 0 minus negative negative negative negative negative left parenthesis 2 right parenthesis comma space 4 straight y plus 3 straight x equals 0 minus negative negative negative negative negative negative left parenthesis 3 right parenthesis . space Find space the space vertices space of space space triangleby space solving space simlutaneously. let space straight A space be space the space point space of space intersection space of space straight y minus 15 equals 0 space and space 12 straight y minus 5 straight x equals 0. let space straight B space be space the space point space of space intersection space of space 12 straight y minus 5 straight x equals 0 space and space 4 straight y plus 3 straight x equals 0. let space straight C space be space the space point space of space intersection space of space straight y minus 15 equals 0 space and space 4 straight y plus 3 straight x equals 0. solving space simultaneously space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space we space get space straight y equals 15 space and space 12 left parenthesis 15 right parenthesis minus 5 straight x equals 0 space implies space straight x equals 36. So space coordinates space of space straight A space is space left parenthesis 36 comma 15 right parenthesis. solving space simultaneously space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis space we space get space straight x equals 0 space and space straight y equals 0 space So space coordinates space of space straight B space is space left parenthesis 0 comma 0 right parenthesis. solving space simultaneously space left parenthesis 1 right parenthesis space and space left parenthesis 3 right parenthesis space we space get space straight y equals 15 space and space 4 left parenthesis 15 right parenthesis plus 3 straight x equals 0 space implies space straight x equals negative 20. So space coordinates space of space straight C space is space left parenthesis negative 20 comma 15 right parenthesis So space triangle space is space formed space by space straight A left parenthesis 36 comma 15 right parenthesis comma space straight B left parenthesis 0 comma 0 right parenthesis space and space straight C left parenthesis negative 20 comma 15 right parenthesis. now space find space the space length space of space AB space space say space straight c comma space BC space space say space straight a space comma and space AC space say space straight b comma space by space distance space formula space square root of left parenthesis straight x subscript 1 minus straight x subscript 2 right parenthesis squared plus left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis squared end root So space straight a equals 25 comma space straight b equals 39 comma straight c equals 56. now space by space formula space for space coordinates space of space incenter space left parenthesis straight h comma straight k right parenthesis equals left parenthesis fraction numerator aA subscript straight x plus bB subscript straight x plus cC subscript straight x over denominator straight a plus straight b plus straight c end fraction space space comma space fraction numerator aA subscript straight y plus bB subscript straight y plus cC subscript straight y over denominator straight a plus straight b plus straight c end fraction right parenthesis space space where space straight A subscript straight x comma space straight B subscript straight x space straight C subscript straight x space are space the space straight x space coordinates space of space straight A space comma straight B space and space straight C space respectively space and space straight A subscript straight y comma space straight B subscript straight y space straight C subscript straight y space end subscript are space the space straight y space coordinate space of space straight A comma space straight B space and space straight C space respectively. so space left parenthesis straight h comma straight k right parenthesis equals left parenthesis fraction numerator 25 left parenthesis 36 right parenthesis plus 39 left parenthesis 0 right parenthesis plus 56 left parenthesis negative 20 right parenthesis over denominator 25 plus 39 plus 56 end fraction comma fraction numerator 25 left parenthesis 15 right parenthesis plus 39 left parenthesis 0 right parenthesis plus 56 left parenthesis 15 right parenthesis over denominator 25 plus 39 plus 56 end fraction right parenthesis equals left parenthesis fraction numerator negative 11 over denominator 6 end fraction comma 223 over 24 right parenthesis equals left parenthesis negative 1.83333 comma 10.125 right parenthesis. end style
Answered by Yasmeen Khan | 08 Oct, 2018, 10:37: PM

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