Question

Find the coordinates of the centroid of a triangle PQR with vertices P(-2,4), Q(4,1), and R(-2,-3).

a) (−0.67,0.67)
b) (0.67,−0.67)
c) (−0.67,−0.67)
d) (0.67,0.67)

Answer 1

The centroid of triangle PQR with given vertices is calculated by averaging the x and y coordinates of the vertices, resulting in the coordinates (0.00, 0.67), which is closest to option (d) (0.67, 0.67).

Step-by-step explanation:

The centroid of a triangle, which is also the center of gravity or geometric center, is found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. For the triangle PQR with vertices P(-2,4), Q(4,1), and R(-2,-3), the centroid will have the x-coordinate calculated as (-2 + 4 - 2)/3, which equals 0, and the y-coordinate calculated as (4 + 1 - 3)/3, which equals 2/3 or approximately 0.67.

So the coordinates of the centroid are (0, 2/3), which when given in decimal form would be approximately (0.00, 0.67). Therefore, the closest answer from the options provided is d) (0.67,0.67).