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 are $(a,b)$. The value of $a+b$, is

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

Answer 1

Answer: (B)

$14$

A] A (7,2) B (1,6) C(a,b)

centroid = $(\frac{7+1+a}{3},\frac{2+6+b}{3})=(4,6)$

$\therefore \frac{7+1+a}{3}=4$

$=\frac{8+a}{3}=4$

$8+a=12$

$a=12-8$

$a=4$

$\frac{2+6+b}{3}=6$

$\frac{8+b}{3}=6$

$8+b=18$

$b=10$

Thus, $a+b=4+10=14$