Question

the mid points of the sides of the triangle AB, BC, CA are (3,1) (5,6) (-3,2) respectively find the vertices of the triangle ABC

Answer 1

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Answer 2

Answer:

$Coordinates \:of \:A,B\:and \:C \:are \\(-5,-3),(5,5) \:and\:(-1,7)$

Step-by-step explanation:

The mid points of the sides of the triangle AB, BC, CA are D(3,1),E(5,6), F(-3,2) respectively

$From \: the \: figure ,\\A(x_{1},y_{1})=\left(x_{4}+x_{6}-x_{5} ,y_{4}+y_{6}-y_{5}\right)\\</p><p>=\left(3-3-5,1+2-6\right)\\=(-5,-3)$

$B(x_{2},y_{2})=\left(x_{4}+x_{5}-x_{6} ,y_{4}+y_{5}-y_{6}\right)\\</p><p>=\left(3+5-3,1+6-2\right)\\=(5,5)$

$C(x_{3},y_{3})=\left(x_{5}+x_{6}-x_{4} ,y_{5}+y_{6}-y_{4}\right)\\</p><p>=\left(5-3-3,6+2-1\right)\\=(-1,7)$

Therefore,

$Coordinates \:of \:A,B\:and \:C \:are \\(-5,-3),(5,5) \:and\:(-1,7)$

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