If (3, 2) are coordinates of the centroid of a triangle, whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.

Correct option is D

Given:

Centroid = (3, 2)

Vertices of triangle: A(0, 4), B(-2, 0), C(p, 2)

Formula Used:

Centroid G of a triangle with vertices $$(x_1, y_1), (x_2, y_2), (x_3, y_3)$$​ is:

G = $$\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$$​​

Solution: 

Centroid = $$\left( \frac{0 + (-2) + p}{3}, \frac{4 + 0 + 2}{3} \right)$$​ = (3, 2)

Y-coordinate: 

​$$=\frac{4 + 0 + 2}{3} = \frac{6}{3} = 2$$​​

X-coordinate:

​$$\frac{-2 + p}{3} = 3 \\ \ \\ -2 + p = 9\\ \ \\ p = 11$$​​