NAME_______________________________________DATE_____________________
GEOMETRY
HOMEWORK: CENTROID
Show all work on loose leaf.
1. State whether the centroid appears on the side of the triangle, in the interior of the triangle, or
in the exterior of the triangle for each of the following.
a) an acute triangle
b) a right triangle
c) an obtuse triangle
In exercises 2-4, find the coordinates of the centroid of the triangle with the given vertices.
2. (-5,4), (1,9), (7,2)
3. (-2,-5), (-1,0), (9,2)
4. (1,-1), (2,6), (7,3)
5. Given DEF with D(-4,3), E(3,-8), and F(10,2), show that the medians of DEF
intersect at (3,-1).
6. In what kind of triangle does the centroid lie outside of the triangle?
Exercises 7-13: QRS with medians QA , RB , and SC concurrent at centroid P.
R
C
Q
P
A
B
7. If RB = 20, find PB.
8. If PC = 12, find SC.
9. If RP = 11, find RB.
10. If QP = 9, find PA.
11. If SP = 2x and SC = 5x + 4, find SP and SC.
12. If PB = 3x and PR = 7x – 5, find PB and PR.
13. If PA = 2x + 6 and QA = 10x, find PA and QA.
S
14. N is the centroid of HIJ . If HL = 7, IM = 5, and HN = 10,
H
a)
b)
c)
d)
e)
find the length of HM
find the length of NK
find the ratio of IN to NL
find the ratio of IN to IL
given HI = IJ, find the perimeter of HIJ
L
M
N
J
K
I
15. Given PQR with medians PT , QU , and RS which intersect at point V:
a) If RS = 12, find RV and VS
b) If VT = 6, find PT and PV
c) If QU = 72 , find QV and VU
16. In ABC , medians AD and CE are concurrent at F. If AF = 4x – 12 and FD = x,
find AF, FD, and AD.
B
D
E
F
C
A
17. In RST , medians RV and TU are concurrent at W. If TU = 3x + 3 and WU = 2x – 3,
find TW, WU, and TU.
R
U
W
T
S
V
18. In MNP , medians NQ and PR are concurrent at O. If NQ = 4x – 10 and NO = x + 5,
find NO, OQ, and NQ.
N
R
O
M
Q
P