Question

Prove that when the three medians of the triangle are drawn, they meet at a single point A(-5,1) B(1,7) C(1,-5). What is the point of the centroid? (1 point) Responses
(−3,1)
(−13,13)
(−12,12)
(−1,1)

Answer 1

To find the centroid of a triangle, we can average the coordinates of the three vertices. Let's label the coordinates of the centroid as G(x, y).

The coordinates of the vertices are:
A: (-5, 1)
B: (1, 7)
C: (1, -5)

To find the x-coordinate of the centroid, we average the x-coordinates of the vertices:
x = (-5 + 1 + 1) / 3 = -3/3 = -1

To find the y-coordinate of the centroid, we average the y-coordinates of the vertices:
y = (1 + 7 - 5) / 3 = 3/3 = 1

Therefore, the coordinates of the centroid are G(-1, 1).

The correct answer is (−1, 1).