NAME
DATE
1-3
PERIOD
Study Guide and Intervention
Locating Points and Midpoints
Midpoint of a Segment
If the coordinates of the endpoints of a segment are x1 and x2,
Midpoint on a
Number Line
x +x
1
2
.
then the coordinate of the midpoint of the segment is −
2
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
Midpoint on a
Coordinate Plane
then the coordinates of the midpoint of the segment are
+x
,
( x−
2
1
2
y +y
)
1
2
−
.
2
−−
Find the coordinate of the midpoint of PQ.
Example 1
P
Q
-3 -2 -1
0
1
2
The coordinates of P and Q are -3 and 1.
−−−
Geo-SG01-03-05-846589
-3 + 1
-2
If M is the midpoint of PQ, then the coordinate of M is − = −
or -1.
2
−−−
Find the coordinates of M, the midpoint of PQ, for P(-2, 4) and
Example 2
Q(4, 1).
+x
y +y
-2 + 4 4 + 1
, − ) = ( − , − ) or (1, 2.5)
( x−
2
2
2
2
1
2
1
2
Exercises
Use the number line to find the coordinate of
the midpoint of each segment.
−−−
1. CE
−−−
2. DG
−−
3. AF
−−−
4. EG
−−
5. AB
−−−
6. BG
−−−
7. BD
−−−
8. DE
A
–10 –8
B
–6
C
–4
–2
D
EF
0
2
G
4
6
8
Geo-SG01-03-06-846589
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8)
10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13)
12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10)
14. K(-11, 2), L(-19, 6)
Chapter 1
18
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
M=
2
NAME
DATE
1-3
PERIOD
Study Guide and Intervention
(continued)
Locating Points and Midpoints
Locate Points
The midpoint of a segment is half the distance from one endpoint to the other. Points
located at other fractional distances from one endpoint can be found using a similar method.
m
If the coordinates of the endpoints of a segment are x1 and x2 and the point is −
n of the
Locating Points
on a Number Line
distance from x1 to x2, then the coordinate of the point is x1
m
If a segment has endpoints A(x1, y1) and B(x2, y2) and the point is −
n of the distance from
Locating Points
on a Coordinate
Plane
Example 1
m⎪x - x ⎥
2
1
+ −
.
n
(
m⎪x2 - x1⎥
m⎪y2 - y1⎥
)
point A to point B, then the coordinates of the point are x1 + −
, y1 + −
.
n
n
1
Find the coordinates of a point −
of the distance from A to B.
3
A
B
-6 -5 -4 -3 -2 -1 0
1
2
3
4
1
The coordinates of A and B are -5 and 2. If P is the point −
of the distance from A to B,
3
⎪2-(-5)⎥
7
-8
then the coordinate of P is -5 + − = -5 + − = − ≈ -2.7.
3
3
3
Example 2
to B(4, 3).
(
1
Find the coordinates of P, a point −
of the distance from A(-2, -4)
4
m⎪x 2 - x 1⎥
m⎪y 2 - y 1⎥
P = x1 + −
, y1 + −
n
n
(
)
(
) = (-2 +
⎪4 - (-2)⎥
4
⎪3 - (-4)⎥
4
− , -4 + −
)
Lesson 1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
P19-001A-890857
)
6
7
1
1
= -2 + −
, -4 + −
or about - −
, -2 −
.
4
4
2
4
Exercises
Use the number line to find the
coordinate of the point the given
fractional distance from A to B.
1
1. −
5
3
4. −
4
A
–10
B
–8
1
2. −
–6
–4
–2
0
2
4
6
8
10
2
3. −
P19-002A-890857
3
3
1
5. −
4
2
6. −
5
−−−
Find P on NM that is the given fractional distance from N to M.
1
; N(-3, -2), M(1, 1)
7. −
5
2
9. −
; N(-7, 3), M(5, 2)
3
1
11. −
; N(-2, 5), M(0, -4)
4
Chapter 1
019_GEOCRMC01_715477.indd 19
1
8. −
; N(-2, -4), M(4, 4)
3
3
10. −
; N(-3, 1), M(2, 6)
4
2
12. −
; N(-2, -1), M(8, 3)
5
19
Glencoe Geometry
2nd Pass
8/7/14 5:40 PM
NAME
1-3
DATE
PERIOD
Skills Practice
Locating Points and Midpoints
Use the number line to find the coordinate
of the midpoint of each segment.
−−−
1. DE
−−−
3. BD
A
–6
−−−
2. BC
−−−
4. AD
–4
B
–2
C
0
2
D
4
E
6
8
10
12
Geo-SG01-03-04-846589
Find the coordinates of the midpoint of a segment with the given endpoints.
5. T(3, 1), U(5, 3)
6. J(-4, 2), F(5, -2)
−−−
Find the coordinates of the missing endpoint if P is the midpoint of NQ.
7. N(2, 0), P(5, 2)
8. N(5, 4), P(6, 3)
Use the number line to find the coordinate of the
point the given fractional distance from A to B.
9. Q(3, 9), P(-1, 5)
-3 -2 -1 0
2
11. −
1
12. −
3
13. −
2
14. −
1
15. −
1
16. −
5
17. −
6
4
3
3
2
3
4
5
6
7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
10. −
1
4
5
5
6
−−−
Find P on NM that is the given fractional distance from N to M.
2
18. −
, N(-3, 1), M(2, 6)
2
19. −
, N(-2, 5), M(0, -4)
1
, N(-2, -1), M(8, 3)
20. −
3
21. −
, N(4, 5), M(-7, 1)
3
4
5
4
A
Refer to the graph at the right.
−−
22. Find C on AB such that the ratio of AC to CB is 2:3.
−−
23. Find C on AB such that the ratio of AC to CB is 1:3.
-4
2
-2
O
20
2
4x
-2
-4
-6
Chapter 1
y
B
Glencoe Geometry
P20-002A-890857
NAME
1-3
DATE
PERIOD
Practice
Locating Points and Midpoints
Use the number line to find the coordinate
of the midpoint of each segment.
P
–10
−−−
2. QR
−−
4. PR
−−
1. RT
−−
3. ST
Q
–8
–6
R
–4
S
–2
T
0
2
4
6
Geo-SG01-03-08-846589
Find the coordinates of the midpoint of a segment with the given endpoints.
5. K(-9, 3), H(5, 7)
6. W(-12, -7), T(-8, -4)
−−
Find the coordinates of the missing endpoint if E is the midpoint of DF.
7. F(5, 8), E(4, 3)
8. F(2, 9), E(-1, 6)
9. D(-3, -8), E(1, -2)
Use the number line to find the coordinate
of the point the given fractional distance
from A to B.
1
11. −
3
3
15. −
5
1
12. −
5
2
16. −
3
A
B
-8 -7 -6 -5 -4 -3 -2 -1 0
1
13. −
6
5
17. −
6
1
2
3
4
5
6
Lesson 1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3),
T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the
nearest tenth.
1
14. −
4
P21-001A-890857
3
18. −
4
−−−
Find P on NM that is the given fractional distance from N to M.
3
, N(1, 7), M(9, -2)
19. −
4
2
, N(-3, -4), M(6, 3)
21. −
5
4
20. −
, N(-4, 5), M(2, -6)
5
1
22. −
, N(-4, 2), M(7, 9)
3
Refer to the graph at the right.
y
−−
23. Find C on AB such that the ratio of AC to CB is 1:2.
B
4
2
−−
24. Find C on AB such that the ratio of AC to CB is 4:3.
-4
-2
O
2
4x
-2
A
Chapter 1
021_GEOCRMC01_715477.indd 21
21
P21-002A-890857
Glencoe Geometry
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7/30/14 5:30 PM