Question

Find the centroid of the triangle whose vertices are $(1,3),(2,7)$ and $(12,-16).$

• A. $(5,-2)$
• B. $(5,2)$
• C. $(-5,-2)$
• D. None of these

Answer 1

Answer: (A)

$(5,-2)$

Consider the given vertices.

$(1,3),(2,7)$ and $(12,-16)$

We know that the centroid of the triangle

$=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

where $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are the vertices of the triangle

So,

$centroid=(\frac{1+2+12}{3},\frac{3+7-16}{3})$

$centroid=(\frac{15}{3},\frac{-6}{3})$

$centroid=(5,-2)$

Hence, this is the answer.