Question

If $(1,4)$ is the centroid of the triangle having the vertices $(a,3),(4,b)$ and $(-3,2)$ then $a=$ _______ and $b=$ _______.

• A. $-7,-2$
• B. $2,7$
• C. $-2,-7$
• D. $-4,2$

Answer 1

The correct option is B $2,7$

$(1,4)$ is the centroid of the triangle having the vertices $(a,3)(4,b)$ and $(-3,2)$

$\therefore (1,4)=(\frac{a+4-3}{3},\frac{3+b+2}{3})$
$\therefore (1,4)=(\frac{a+1}{3},\frac{b+5}{3})$

$\therefore \frac{a+1}{3}=1,\frac{b+5}{3}=4$

$\therefore a+1=3b+5=12$

$\therefore a=2b=7$.