Question
Find the centroid of the triangle whose vertices are:
$(1, 4) (-1, -1), (3, -2).$
$(1, 4) (-1, -1), (3, -2).$
✓
Answer
We know that the coordinates of the centroid of a triangle whose vertices are $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ are,
$\Big(\frac{\text{x}_1+\text{x}_2+\text{x}_3}{3},\frac{\text{y}_1+\text{y}_2+\text{y}_3}{3}\Big)$
So, the coordinates of the centroid of a triangle whose vertices are $(1, 4), (-1, -1)$ and $(3, -2)$ are $\Big(\frac{1-1+3}{3},\frac{4-1-2}{3}\Big)$
$=\Big(1,\frac{1}{3}\Big)$
$\Big(\frac{\text{x}_1+\text{x}_2+\text{x}_3}{3},\frac{\text{y}_1+\text{y}_2+\text{y}_3}{3}\Big)$
So, the coordinates of the centroid of a triangle whose vertices are $(1, 4), (-1, -1)$ and $(3, -2)$ are $\Big(\frac{1-1+3}{3},\frac{4-1-2}{3}\Big)$
$=\Big(1,\frac{1}{3}\Big)$
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