Question

If $(-2,3),(4,-3),(4,5)$ are mid-points of the sides of a triangle, find the coordinates of the centroid of the triangle formed by these mid-points.

• A. $(3,\frac{4}{3})$
• B. $(2,\frac{4}{3})$
• C. $(2,\frac{5}{3})$
• D. $(3,\frac{5}{3})$

Answer 1

Answer: (C)

$(2,\frac{5}{3})$

Let the given vertices of a triangle be A$(-2,3)$ and B $(4,-3)$ let the third vertex be C $(4,5)$.

Let Centroid be $G=[\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}]$

$\Rightarrow G$ = $(\frac{-2+4+4}{3},\frac{3-3+5}{3})$

$\Rightarrow G$ = $(\frac{6}{3},\frac{5}{3})$

$\Rightarrow G$ = $(2,\frac{5}{3})$.