Question

In the adjoining diagram, G is the centroid of ΔABC. A(3, –3), В(2, –6), C(x, y) and G(5, –5). The coordinates of point D are:

Options

• (2, –6)

• (3, –6)

• (6, –6)

• (10, –6)

Answer 1

(6, –6)

Explanation:

The centroid G has coordinates equal to the average of the vertices.

So, `((3 + 2 + x)/3, (-3 + (-6) + y)/3) = (5, −5)`. 

Solving gives x = 10 and y = –6.

Point D is the midpoint of BC.

So, D = `((2 + 10)/2, (-6 + (-6))/2) = (6, -6)`.