Question : The coordinate of the centroid of a $\triangle$ABC is (2, 2). What are the coordinates of vertex C, if the coordinates of A and B are (7, –1) and (1, 2), respectively?
Option 1: (–2, 5)
Option 2: (2, 5)
Option 3: (–2, –5)
Option 4: (2, –5)
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Correct Answer: (–2, 5)
Solution :
Given: The coordinates of the centroid of a $\triangle ABC$ are (2, 2). The coordinates of A and B are (7, –1) and (1, 2) respectively.
Let $(x,y)$ be the coordinates of C.
$\triangle ABC$ centroid can be expressed as $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.
In terms of the $x$ coordinate, $2=\frac{x+7+1}{3}$.
⇒ $x = 6–8$
⇒ $x = –2$
About the $y$ coordinate, $2=\frac{y–1+2}{3}$.
⇒ $y = 6–1$
⇒ $y = 5$
The C coordinate is (–2, 5).
Hence, the correct answer is (–2, 5).
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