Question

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

• A. $(-1,\frac{7}{3})$
• B. $(\frac{-1}{3},\frac{7}{3})$
• C. $(1,\frac{7}{3})$
• D. $(\frac{1}{3},\frac{7}{3})$

Answer 1

Answer: (C)

$(1,\frac{7}{3})$

Vertex of triangle is $(1,1)$ and midpoint of sides through this vertex is $(-1,2)$ and $(3,2)$

Co-ordinate of B is (x,y)

co-ordinates of B is$(\frac{1+x}{2}=-1,\frac{1+y}{2}=1)::\left(\right(x,y):(-3,3\left)\right)$
Similarly, co-ordinate of C comes out to be (5,3)

Thus centroid is, $\frac{1-3+5}{3},\frac{1+3+3}{3}\Rightarrow (1,\frac{7}{3})$ ...(hint: using formula of centroid)