MATH HIGH SCHOOL
COORDINATE GEOMETRY
EXERCISES
High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
EXERCISES
EXERCISES
For problems 1–3, choose the correct ratio that the given segment has been partitioned
into by point S.
y
1.
5
4
3
2
1
S
–7 –6 –5 –4 –3 –2 –1
–2
A
–3
–4
–5
B
1 2 3 4 5 6 7 8 x
A 1:1
B 1:2
C 1:3
D 1:4
y
2.
S
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
D
–2
–3
–4
–5
E
1 2 3 4 5 6 7 8 x
A 1:5
B 2:5
C 2:3
D 3:5
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High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
EXERCISES
y
3.
G
6
4
2
S
–6
–4
–2
4
2
6
x
–2
–4
–6
–8
H
A 3:7
B 3:4
C 4:7
D 3:5
For questions 4–6, plot the given points, and determine the point P that will partition the
segment by the given ratio.
4. Point A = (0, 5), point B = (0, –10), partition segment AB by a ratio of 7:8.
5.
Point C = (–8,–2), point D = (4, 1), partition segment CD by a ratio of 2:1.
6. Point E = (–6, 4) point F = (8, –8), partition segment EF by a ratio of 1:3.
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11
High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
7.
EXERCISES
Using the points P (–5,–3), Q(7, 4), and M(4, 2.25):
•
Compute the distance from P to M, and the distance from M to Q.
•
Find the ratio of the length PM to the length MQ.
Challenge Problem
8. Draw the segment TV where T = (–7, –7) and V = (9, 1).
Copyright © 2014 Pearson Education, Inc.
•
Use the partitioning formula to find the coordinates of the point U that partitions
the segment TV by a ratio of 3:5.
•
Plot point U on your graph.
12
MATH HIGH SCHOOL
COORDINATE GEOMETRY
ANSWERS
EXERCISES
FOR EXERCISES
High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
ANSWERS
ANSWERS
1.
B 1:2
2.
C 2:5
3.
B 3:7
y
4.
6
A
4
2
–4
–2
2
x
4
P
–2
–4
–6
–8
–10
B
y
5.
4
2
D
P
–10
–8
–6
–4
–2
2
–2
C
–4
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44
4
6
x
High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
6.
ANSWERS
y
E
4
2
P (–2.5,1)
–6
–4
–2
2
4
6
10 x
8
–2
–4
–6
–8
F
–10
7.
y
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–2
–3
P (–5, –3) –4
Q (7, 4)
M (4, 2.25)
1 2 3 4 5 6 7 8 x
(rounded to thousandths):
Length of PM = 10.419
Length of MQ = 3.473
The ratio is 1:2.
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High School: Coordinate Geometry
LESSON 3: PARTITIONING LINE SEGMENTS
ANSWERS
Challenge Problem
8. Use the partitioning formula for point U, where T = (–7, –7) and V = (9, 1) and the
partition is by a ratio of 3:5.
⎡ (3)( 9 ) + ( 5) ( −7 ) (3)(1) + ( 5) ( −7 ) ⎤
U=⎢
,
⎥
3+5
3+5
⎣
⎦
U = (–1, –4)
y
2
–8
–6
–4
V
–2
2
–2
U (–1, –4)
–4
–6
T
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–8
46
4
6
8
10 x