Question : What are the coordinates of the centroid of a triangle whose vertices are A (2, 5), B (–4, 0), and C (5, 4)?
Option 1: (–1, 3)
Option 2: (1, 3)
Option 3: (1, –3)
Option 4: (–1, –3)
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Correct Answer: (1, 3)
Solution :
Given: The vertices are A(2, 5), B(–4, 0), and C(5, 4).
The centroid coordinates = $(x, y)$ = $\frac{(x_{1} + x_{2} + x_{3})}{3}, \frac{(y_{1} + y_{2} + y_{3})}{3}$.
Centroid coordinates $(x, y)$ = $\frac{(2 – 4 + 5)}{3}, \frac{(5 + 0 + 4)}{3}$.
Centroid coordinates $(x, y)$ = (1, 3)
So, the coordinates of the centroid of the triangle ABC are (1, 3).
Hence, the correct answer is (1, 3).
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