Question

30. D(3, 2), E(5, 6) and F(-1, 7) are the midpoints of the sides BC, CA and AB of triangle ABC respectively. Find the
coordinates of A, B and C.​

Answer 1

$Let \: A(x_{1}, y_{1}) , B(x_{2}, y_{2}) \:and\\ \:C(x_{3}, y_{3}) \: are \: vertices \:of \: triangle \\ABC .\\D(a,b) = (3,2) , \:E(c,d) = (5,6) ,\:and \\F(e,f) = (-1,7) \: are \: mid - points \: of \: BC, CA \:and \: AB\\respectively .$

$A(x_{1}, y_{1}) = ( e + c - a, f + d - b) \\= ( -1+5-3,7+6-2)\\= ( 1 , 11)$

$B(x_{2}, y_{2}) = ( e +a-c, f+b-d) \\= ( -1+3-5,7+2-6)\\= ( -3 , 3)$

$C(x_{3}, y_{3}) = ( a+c-e, b+d-f) \\= ( 3+5+1,2+6-7)\\= ( 9,1)$

Therefore.,

$\red{ Coordinates \:of \: A,B \:and \:C \:are }$

$\green { (1,11) , (-3,3) \:and \:(9,1) }$

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