Question

Find the centroid of the triangle with these vertices: P (-4,10), Q (8,6), and R (2,6).

The coordinates of the centroid are ______?

A. (2, 7.33)
B. (2, 7)
C. (2, 7.5)
D. (2, 7.7)

Answer 1

To find the centroid of a triangle, use the formula (x-coordinate of A + x-coordinate of B + x-coordinate of C) / 3 for the x-coordinate and (y-coordinate of A + y-coordinate of B + y-coordinate of C) / 3 for the y-coordinate. For the given triangle with coordinates P (-4,10), Q (8,6), and R (2,6), the centroid is approximately (2, 7.33).

Step-by-step explanation:

To find the centroid of a triangle, we can use the formula:

x-coordinate of the centroid = (x-coordinate of A + x-coordinate of B + x-coordinate of C) / 3

y-coordinate of the centroid = (y-coordinate of A + y-coordinate of B + y-coordinate of C) / 3

Using the given coordinates:

x-coordinate of the centroid = (-4 + 8 + 2) / 3 = 6 / 3 = 2

y-coordinate of the centroid = (10 + 6 + 6) / 3 = 22 / 3 ≈ 7.33

Therefore, the coordinates of the centroid are approximately (2, 7.33).