If the vertex of triangle is (-8,-17) and mid-points of two sides throught it be (2,1) and (-1,3) then find the other two vertices and the mid point. (CBSE March 2014)

Asked by Ŝũmiť Ğőyãĺ | 14th Nov, 2014, 10:15: PM

Expert Answer:

L e t space A B C space b e space t h e space g i v e n space t r i a n g l e. L e t space t h e space c o o r d i n a t e s space o f space B space a r e space x subscript 1 space a n d space y subscript 1 A n d space t h e space c o o r d i n a t e s space o f space C space a r e space x subscript 2 space a n d space y subscript 2 G i v e n space t h a t space t h e space c o o r d i n a t e s space o f space D space a r e space 2 space a n d space 1 T h u s comma space f r o m space t h e space d i a g r a m space i t space i s space c l e a r space t h a t fraction numerator minus 8 plus x subscript 1 over denominator 2 end fraction equals 2 ; fraction numerator minus 17 plus y subscript 1 over denominator 2 end fraction equals 1 ; fraction numerator minus 8 plus x subscript 2 over denominator 2 end fraction equals minus 1 ; fraction numerator minus 17 plus y subscript 2 over denominator 2 end fraction equals 3 rightwards double arrow minus 8 plus x subscript 1 equals 4 ; minus 17 plus y subscript 1 equals 2 ; minus 8 plus x subscript 2 equals minus 2 ; minus 17 plus y subscript 2 equals 6 rightwards double arrow x subscript 1 equals 4 plus 8 ; y subscript 1 equals 2 plus 17 ; x subscript 2 equals minus 2 plus 8 ; y subscript 2 equals 6 plus 17 rightwards double arrow x subscript 1 equals 12 ; y subscript 1 equals 19 ; x subscript 2 equals 6 ; y subscript 2 equals 23 T h u s comma space t h e space c o o r d i n a t e s space o f space B space a n d space C space a r e space open parentheses 12 comma 19 close parentheses space a n d space open parentheses 6 comma 23 close parentheses space r e s p e c t i v e l y. M i d p o i n t space o f space B space a n d space C space i s space F space a n d space t h e space c o o r d i n a t e s space o f space F space a r e : space fraction numerator 12 plus 6 over denominator 2 end fraction space a n d space fraction numerator 19 plus 23 over denominator 2 end fraction ; rightwards double arrow 18 over 2 space a n d space 42 over 2 rightwards double arrow x equals 9 space a n d space y equals 21

Answered by Vimala Ramamurthy | 15th Nov, 2014, 01:32: PM

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