Find the sum of 'x' co-ordinates of the vertices of a triangle if the mid-points of its sides be the points $(6, - 1), (- 1, - 2) a n d (1, - 4)$

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Solution

$\frac{x_{2} + x_{3}}{2} = 6, \frac{y_{2} + y_{3}}{2} = - 1.$
$∴ x_{2} + x_{3} = 12, x_{3} + x_{1} = - 2, x_{1} + x_{2} = 2.$
$∴ 2 (x_{1} + x_{2} + x_{3}) = 12.$
or $x_{1} + x_{2} + x_{3} = 6$

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