Question

Find the values of a and b if (3, 6) is the centroid of the triangle whose vertices are (2, a), (b, 1), and (1, 4).

• A. a = 6, b = 7
• B. a = 6, b = 13
• C. a = 7, b = -9
• D. a = 13, b = 6

Answer 1

The correct option is D a = 13, b = 6

Given:
Centroid is (3, 6) and vertices of triangle are (2, a), (b, 1), and (1, 4).

We know that centroid of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.

So,
(3, 6) = $(\frac{2+b+1}{3},\frac{a+1+4}{3})$
3 = $\frac{2+b+1}{3}$ and 6 = $\frac{a+1+4}{3}$
9 = 3 + b and 18 = a + 5
b = 6 and a = 13