Question

If the two vertices of a triangle are $(7,2)$ and $(1,6)$ and its centroid is $(4,6)$ then the coordinate of the third vertex is $(a,b)$. The value of $(a+b)$, is-

• A. $13$
• B. $14$
• C. $15$
• D. $16$

Answer 1

The correct option is B $14$

Third vertex =(a,b)

$x$ coordinate of centroid =$\frac{x_1+x_2+a}{3}$

$y$ coordinate of centroid =$\frac{y_1+y_2+b}{3}$

$3x=x_1+x_2+a,3y=y_1+y_2+b$

put the values,

$4\left(3\right)=7+1+a$ , $3\left(6\right)=2+6+b$

$a=12-8$ , $b=18-8$

$a=4$ , $b=10$

$a+b=14$