Question

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

(−1, 53)
open paren negative 1 comma 5 thirds close paren

(0, 53)
open paren 0 comma 5 thirds close paren

(0, 0)
open paren 0 comma 0 close paren

(0,−13)
open paren 0 comma negative 1 third close paren
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Answer 1

The centroid is the average of the vertices' coordinates:
x = (-2 + 4 + (-2))/3 = 0/3 = 0
y = (-3 + 0 + 2)/3 = (-1)/3

So the medians meet at (0, −1/3). (Choose the option labeled (0,−13).)