In $△$ ABC , G(-4, -7) is the centroid. If the coordinates of A and B are (-14, -19) and (3, 5) respectively, then find the co-ordinates of C.

(-1, 7)

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(-1, -7)

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(-2, -7)

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(1, 7)

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Solution

The correct option is B (-1, -7)
Given:
Centroid, $G (- 4, - 7)$
Vertex, $A (- 14, - 19) & B (3, 5)$

Let the Co-ordinates of $C$ be $(x_{3}, y_{3})$
$x_{1} = - 14, x_{2} = 3, y_{1} = - 19 & y_{2} = 5$

Centroid
$G (- 4, - 7) = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$

$\Rightarrow \frac{- 14 + 3 + x_{3}}{3} = - 4$
$\Rightarrow x_{3} - 11 = - 12 \Rightarrow x_{3} = - 1$

and $\frac{- 19 + 5 + y_{3}}{3} = - 7$
$\Rightarrow y_{3} - 14 = - 21 \Rightarrow y_{3} = - 7$

$∴$ Co-ordinates of $C$ are $(- 1, - 7)$

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