Question

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

• A. $(1,7/3)$
• B. $(1/3,7/3)$
• C. $(-1,7/3)$
• D. $(-1,7/3)$

Answer 1

The correct option is A

$(1,7/3)$

To find the centroid of the triangle:

Given that, the vertex of a triangle $(1,1)$and the midpoints of two sides through the vertex are $(-1,2)$and$(3,2)$.

Let the coordinates of $B$be$(x,y)$

Now since $(-1,2)$is the midpoint of $(1,1)$and $(x,y)$

So, $\left(\frac{1+x}{2}=-1,\frac{1+y}{2}=2\right)$$\Rightarrow x=-3,y=3$

Hence, the coordinates of $B$is $(x,y)=(-3,3)$

Similarly the coordinates of$C$, we get$(5,3)$

Thus, the centroid of a triangle$=\left(\frac{1-3+5}{3},\frac{1+3+3}{3}\right)=\left(1,7/3\right)$

Hence, The correct option is C.