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Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________
Coordinate Geometry and the Centroid
Find coordinates of the centroid of each triangle.
1)
−7 −6 −5 −4 −3 −2 −1
1
2
3
4
Z
Y
X
2)
−6 −5 −4 −3 −2 −1 1 2 3
1
2
3
4
5
6
7
D
E
F
3)
−7 −6 −5 −4 −3 −2 −1
1
2
3
4
5
6
7
P
Q
R
4)
−3 −2 −1 1 2 3 4 5 6
−7
−6
−5
−4
−3
−2
−1
M
L
K
5)
−2 −1 1 2 3 4 5 6 7
1
2
3
4
5
R
S
T
6)
−3 −2 −1 1 2
−5
−4
−3
−2
−1
K
L
M
-1-
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Worksheet by Kuta Software LLC
7)
−3 −2 −1 1 2 3 4 5 6
−5
−4
−3
−2
−1
1
2
U
V
W
8)
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
R
S
T
Find the coordinates of the centroid of each triangle given the three vertices.
9) C
(
−7, −6
)
, B
(
−8, 0
)
, A
(
0, 0
)
10) S
(
0, −6
)
, R
(
−10, −6
)
, Q
(
1, 0
)
11) T
(
0, 0
)
, U
(
1, 3
)
, V
(
−2, 0
)
12) Y
(
3, 4
)
, X
(
−5, 0
)
, W
(
0, 0
)
13) E
(
6, −3
)
, D
(
−5, −3
)
, C
(
6, −1
)
14) F
(
−7, −3
)
, G
(
−7, −5
)
, H
(
−3, −3
)
Critical thinking questions:
15) Two vertices of a triangle are
(
0, 0
)
and
(
9, 0
)
. The centroid is
(
6, 1
)
. Find the third
vertex of the triangle.
16) For question #1, connect the midpoints of
each side of the triangle to form a smaller
triangle within the original triangle. Find
the coordinates of the centroid of the
smaller triangle. What happened and why?
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________
Coordinate Geometry and the Centroid
Find coordinates of the centroid of each triangle.
1)
−7 −6 −5 −4 −3 −2 −1
1
2
3
4
Z
Y
X
(
−2, 1
)
2)
−6 −5 −4 −3 −2 −1 1 2 3
1
2
3
4
5
6
7
D
E
F
(
−1, 2
)
3)
−7 −6 −5 −4 −3 −2 −1
1
2
3
4
5
6
7
P
Q
R
(
−3, 4
)
4)
−3 −2 −1 1 2 3 4 5 6
−7
−6
−5
−4
−3
−2
−1
M
L
K
(
1, −2
)
5)
−2 −1 1 2 3 4 5 6 7
1
2
3
4
5
R
S
T
(
5
3
,
4
3
)
6)
−3 −2 −1 1 2
−5
−4
−3
−2
−1
K
L
M
(
−
1
3
,
−
4
3
)
-1-
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Worksheet by Kuta Software LLC
7)
−3 −2 −1 1 2 3 4 5 6
−5
−4
−3
−2
−1
1
2
U
V
W
(
4
3
,
−
7
3
)
8)
1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
R
S
T
(
3,
10
3
)
Find the coordinates of the centroid of each triangle given the three vertices.
9) C
(
−7, −6
)
, B
(
−8, 0
)
, A
(
0, 0
)
(
−5, −2
)
10) S
(
0, −6
)
, R
(
−10, −6
)
, Q
(
1, 0
)
(
−3, −4
)
11) T
(
0, 0
)
, U
(
1, 3
)
, V
(
−2, 0
)
(
−
1
3
, 1
)
12) Y
(
3, 4
)
, X
(
−5, 0
)
, W
(
0, 0
)
(
−
2
3
,
4
3
)
13) E
(
6, −3
)
, D
(
−5, −3
)
, C
(
6, −1
)
(
7
3
,
−
7
3
)
14) F
(
−7, −3
)
, G
(
−7, −5
)
, H
(
−3, −3
)
(
−
17
3
,
−
11
3
)
Critical thinking questions:
15) Two vertices of a triangle are
(
0, 0
)
and
(
9, 0
)
. The centroid is
(
6, 1
)
. Find the third
vertex of the triangle.
(
9, 3
)
16) For question #1, connect the midpoints of
each side of the triangle to form a smaller
triangle within the original triangle. Find
the coordinates of the centroid of the
smaller triangle. What happened and why?
Centroid stays the same. The medians don't change.
-2-
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