Question

Triangle ABC
𝐴
𝐵
𝐶
is drawn on a coordinate plane with vertices A(−2,−3)
𝐴
(
−
2
,
−
3
)
, B(4, 0)
𝐵
(
4
,

0
)
, and C(−2, 2)
𝐶
(
−
2
,

2
)
and medians indicating the midpoint of each of the line segments AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
, BC¯¯¯¯¯¯¯¯
𝐵
𝐶
¯
, and CA¯¯¯¯¯¯¯¯
𝐶
𝐴
¯
. Prove that the medians meet at a single point by finding the centroid. (1 point)
Responses

(0,−13)
(
0
,
−
1
3
)

open paren 0 comma negative 1 third close paren

(0, 0)
(
0
,

0
)

open paren 0 comma 0 close paren

(0, 53)
(
0
,

5
3
)

open paren 0 comma 5 thirds close paren

(−1, 5/3)

Answer 1

The centroid (intersection of the medians) is the average of the vertex coordinates:
x = (−2 + 4 + (−2))/3 = 0, y = (−3 + 0 + 2)/3 = −1/3.
So the medians meet at (0, −1/3).