The midpoints of the sides BC,CA & AB of a triangle are D(2,1),E(-5.7) & F(-5,-5)respectively. Find the equations of the sides of triangle ABC.

Asked by Ravikant | 8th Nov, 2015, 09:06: AM

Expert Answer:

G i v e n space t h a t space D left parenthesis 2 comma 1 right parenthesis comma space E left parenthesis negative 5 comma 7 right parenthesis space a n d space F left parenthesis negative 5 comma negative 5 right parenthesis space a r e space t h e space m i d p o i n t s space o f space t h e space s i d e s space B C comma space C A space a n d space A B space o f space t h e space t r i a n g l e space A B C. L e t space A left parenthesis x subscript 1 comma y subscript 1 right parenthesis comma space B open parentheses x subscript 2 comma y subscript 2 close parentheses space a n d space C left parenthesis x subscript 3 comma y subscript 3 right parenthesis space b e space t h e space v e r t i c e s space o f space t h e space t r i a n g l e. T h u s comma space fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction equals negative 5... left parenthesis 1 right parenthesis fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction equals negative 5... left parenthesis 2 right parenthesis fraction numerator x subscript 2 plus x subscript 3 over denominator 2 end fraction equals 2... left parenthesis 3 right parenthesis fraction numerator y subscript 2 plus y subscript 3 over denominator 2 end fraction equals 1... left parenthesis 4 right parenthesis fraction numerator x subscript 1 plus x subscript 3 over denominator 2 end fraction equals negative 5... left parenthesis 5 right parenthesis fraction numerator y subscript 1 plus y subscript 3 over denominator 2 end fraction equals 7... left parenthesis 6 right parenthesis T h u s space s o l v i n g space t h e space a b o v e space e q u a t i o n s comma space w e space g e t comma x subscript 1 equals negative 12 comma space y subscript 1 equals 1 x subscript 2 equals 2 comma space y subscript 2 equals negative 11 x subscript 3 equals 2 comma space y subscript 3 equals negative 13 W e space k n o w space t h a t space e q u a t i o n space o f space a space l i n e space j o i n i n g space t w o space p o i n t s space i s fraction numerator x minus x subscript 1 over denominator x subscript 1 minus x subscript 2 end fraction equals fraction numerator y minus y subscript 1 over denominator y subscript 1 minus y subscript 2 end fraction T h u s space e q u a t i o n space o f space t h e space l i n e space j o i n i n g space t w o space p o i n t s space A open parentheses negative 12 comma 1 close parentheses space a n d space B open parentheses 2 comma negative 11 close parentheses space i s fraction numerator x plus 12 over denominator negative 12 minus 2 end fraction equals fraction numerator y minus 1 over denominator 1 plus 11 end fraction rightwards double arrow 6 x plus 7 y plus 65 equals 0  T h u s space e q u a t i o n space o f space t h e space l i n e space j o i n i n g space t w o space p o i n t s space B open parentheses 2 comma negative 11 close parentheses space a n d space C open parentheses 2 comma 13 close parentheses space i s fraction numerator x minus 2 over denominator 2 minus 2 end fraction equals fraction numerator y plus 11 over denominator negative 11 minus 13 end fraction rightwards double arrow x equals 2  T h u s space e q u a t i o n space o f space t h e space l i n e space j o i n i n g space t w o space p o i n t s space C open parentheses 2 comma 13 close parentheses space a n d space A open parentheses negative 12 comma 1 close parentheses space i s fraction numerator x minus 2 over denominator 2 plus 12 end fraction equals fraction numerator y minus 13 over denominator 13 minus 1 end fraction rightwards double arrow 6 x minus 7 y plus 79 equals 0

Answered by Vimala Ramamurthy | 9th Nov, 2015, 12:22: PM