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Q) Consider a triangle with vertices A(1,2), B(3,1)& C(-3,0).Find the equation of internal angle bisector of angle A.

Asked by araima2001 15th February 2017, 12:57 PM
Answered by Expert
Answer:
begin mathsize 16px style The space given space vertices space of space straight a space triangle space ABC space are space straight A left parenthesis 1 comma space 2 right parenthesis comma space straight B left parenthesis 3 comma space 1 right parenthesis space and space straight C left parenthesis negative 3 comma space 0 right parenthesis.
Equation space of space line space AB space is space given space by
straight y minus straight y subscript 1 equals fraction numerator straight y subscript 2 minus straight y subscript 1 over denominator straight x subscript 2 minus straight x subscript 1 end fraction left parenthesis straight x minus straight x subscript 1 right parenthesis
rightwards double arrow straight y minus 2 equals fraction numerator 1 minus 2 over denominator 3 minus 1 end fraction left parenthesis straight x minus 1 right parenthesis
rightwards double arrow straight y minus 2 equals fraction numerator negative 1 over denominator 2 end fraction left parenthesis straight x minus 1 right parenthesis
rightwards double arrow 2 straight y minus 4 equals negative straight x plus 1
rightwards double arrow straight x plus 2 straight y minus 5 equals 0 space space space
Equation space of space line space CA space is space given space by
straight y minus straight y subscript 1 equals fraction numerator straight y subscript 2 minus straight y subscript 1 over denominator straight x subscript 2 minus straight x subscript 1 end fraction left parenthesis straight x minus straight x subscript 1 right parenthesis
rightwards double arrow straight y minus 0 equals fraction numerator 2 minus 0 over denominator 1 plus 3 end fraction left parenthesis straight x plus 3 right parenthesis
rightwards double arrow straight y equals 2 over 4 left parenthesis straight x plus 3 right parenthesis
rightwards double arrow 2 straight y equals straight x plus 3
rightwards double arrow straight x minus 2 straight y plus 3 equals 0 space space space space space
Now comma space equation space of space internal space angle space bisector space of space angle space straight A space is space given space by
fraction numerator straight x plus 2 straight y minus 5 over denominator square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end fraction equals fraction numerator straight x minus 2 straight y plus 3 over denominator square root of left parenthesis 1 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root end fraction
rightwards double arrow fraction numerator straight x plus 2 straight y minus 5 over denominator square root of 5 end fraction equals fraction numerator straight x minus 2 straight y plus 3 over denominator square root of 5 end fraction
rightwards double arrow straight x plus 2 straight y minus 5 equals straight x minus 2 straight y plus 3
rightwards double arrow 4 straight y equals 8
rightwards double arrow straight y equals 2 end style
Answered by Expert 15th February 2017, 3:08 PM
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