Question

If a vertex of a triangle is (1, 1) and the middle points of two sides passing through it are (–2, 3) and (5, 2), then find coordinates of centroid of the triangle.

• A. $(5,3)$
• B. $(5,1)$
• C. $(\frac{5}{3},3)$
• D. $(3,1)$

Answer 1

The correct option is C

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

Let the coordinates of B and C be $(\alpha ,\beta )$ and $(\gamma ,\delta )$ respectively.

Then, $-2=\frac{1+\alpha }{2},$ $3=\frac{1+\beta }{2}$

$5=\frac{1+\gamma }{2},$ $2=\frac{1+\delta }{2}$

$\alpha =-5,\beta =5,\gamma =9,\delta =3$

Centroid is

$(\frac{1-5+9}{3},\frac{1+5+3}{3})=(\frac{5}{3},3)$