Triangle ABC is drawn on a coordinate plane with vertices A(−2,−3) , B(4, 0) , and C(−2, 2) and medians indicating the midpoint of each of the line segments AB¯¯¯¯¯¯¯¯ , BC¯¯¯¯¯¯¯¯ , and CA¯¯¯¯¯¯¯¯ . Prove that the medians meet at a single point by finding the centroid. (1 point) Responses
(0,−1/3)
(0, 5/3)
(0, 0)
(−1, 5/3)
To find the coordinates of the centroid, we need to find the average of the x-coordinates and the average of the y-coordinates of the three vertices.
The x-coordinate of the centroid is calculated by adding the x-coordinates of the vertices and dividing by 3:
x-coordinate of centroid = (x-coordinate of A + x-coordinate of B + x-coordinate of C) / 3
= (-2 + 4 + (-2)) / 3
= 0 / 3
= 0.
The y-coordinate of the centroid is calculated by adding the y-coordinates of the vertices and dividing by 3:
y-coordinate of centroid = (y-coordinate of A + y-coordinate of B + y-coordinate of C) / 3
= (-3 + 0 + 2) / 3
= -1 / 3.
Therefore, the coordinates of the centroid are (0, -1/3). Hence, the correct response is (0, -1/3).