Question

Triangle ABC
𝐴
𝐵
𝐶
is drawn on a coordinate plane with vertices A(−3,−3)
𝐴
(
−
3
,
−
3
)
, B(0,6)
𝐵
(
0
,
6
)
, and C(4,−3)
𝐶
(
4
,
−
3
)
and medians indicating the midpoint of each of the lines AB
𝐴
𝐵
, BC
𝐵
𝐶
, and CA
𝐶
𝐴
. Prove the medians meet at a single point by finding the centroid.(1 point)
Responses

(16,3)
(
1
6
,
3
)

left parenthesis Start Fraction 1 over 6 End Fraction comma 3 right parenthesis

(13,1)
(
1
3
,
1
)

left parenthesis Start Fraction 1 over 3 End Fraction comma 1 right parenthesis

(0,13)
(
0
,
1
3
)

left parenthesis 0 comma Start Fraction 1 over 3 End Fraction right parenthesis

(13,0)
(
1
3
,
0
)

left parenthesis Start Fraction 1 over 3 End Fraction comma 0 right parenthesis

Answer 1

The centroid is the average of the vertices:
x = (-3 + 0 + 4)/3 = 1/3, y = (-3 + 6 + (-3))/3 = 0.
So the medians meet at (1/3, 0).

(You can verify this point lies on the median from A to midpoint of BC and on the median from B to midpoint of AC.)