NAME DATE PERIOD Study Guide and Intervention
NAME
DATE
1-3 Study Guide and Intervention
Locating Points and Midpoints
Midpoint of a Segment
PERIOD
Midpoint on a Number Line
Midpoint on a Coordinate Plane
If the coordinates of the endpoints of a segment are x1 and x2, then the coordinate of the midpoint of the segment is x- 1 +2x2 . If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
( ) then the coordinates of the midpoint of the segment are x- 1 +2x2 , - y1 +2 y2 .
Example 1 Find the coordinate of the midpoint of P-Q-.
P
Q
-3 -2 -1 0 1 2
The coordinates of P and Q are -3 and 1. If MGeios-tShGe 0m1i-d0p3o-i0n5t-o8f4-P6-Q5-8, 9then the coordinate of M is -- 3 2+ 1 = - -22 or -1.
Example 2 Find the coordinates of M, the midpoint of P--Q-, for P(-2, 4) and Q(4, 1).
( ) ( ) M = x- 1+2x2 , y- 1+2y2 = -- 2 2+ 4 , 4- +2 1 or (1, 2.5)
Exercises
Use the number line to find the coordinate of the midpoint of each segment.
1. C--E-
2. D--G-
3. A-F-
4. E--G-
5. A-B-
6. B--G-
7. B--D-
8. D--E-
AB C
D EF
G
?10 ?8 ?6 ?4 ?2 0 2 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)
Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 1
18
Glencoe Geometry
NAME
1-3
DATE
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.
Locating Points on a Number Line
Locating Points on a Coordinate Plane
If the coordinates of the endpoints of a segment are x1 and x2 and the point is -mn of the
distance from x1 to x2, then the coordinate of the point is x1 + - mx2n- x1 .
If a segment has endpoints A(x1, y1) and B(x2, y2) and the point is -mn of the distance from
( ) point A to point B, then the coordinates of the point are x1 + - mx2n- x1 , y1 + - my2n- y1 .
Example 1
A
Find the coordinates of a point -13 of the distance from A to B.
B
-6 -5 -4 -3 -2 -1 0 1 2 3 4
The coordinates of A and B are -5 and 2. If P is
P19-001A-890857 then the coordinate of P is -5 +
- 2-(3-5) = -5
the + -73
point -13 = - -38
of the distance -2.7.
from
A
to
B,
Example 2 to B(4, 3).
Find the coordinates of P, a point -14 of the distance from A(-2, -4)
( ) ( ) P = x1 + - mx2n- x1 , y1 + - my2n- y1 = -2 + - 4 -4(-2) , -4 + - 3 -4(-4)
( ) ( ) = -2 + -64, -4 + -74 or about - -12, -2 -14 .
Exercises
Use the number line to find the coordinate of the point the given fractional distance from A to B.
A
B
?10 ?8 ?6 ?4 ?2 0 2 4 6 8 10
1. -15
2. -13
P19-0032.A-23-890857
4. -34
5. -14
6. -25
Find P on -N-M- that is the given fractional distance from N to M.
7. -15; N(-3, -2), M(1, 1)
8. -31; N(-2, -4), M(4, 4)
9. -23; N(-7, 3), M(5, 2)
10. -34; N(-3, 1), M(2, 6)
11. -14; N(-2, 5), M(0, -4)
Chapter 1
12. -25; N(-2, -1), M(8, 3) 19
Glencoe Geometry
Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-3
019_GEOCRMC01_715477.indd 19
2nd Pass
8/7/14 5:40 PM
NAME
1-3 Skills Practice
DATE
PERIOD
Locating Points and Midpoints
Use the number line to find the coordinate of the midpoint of each segment.
1. D--E- 3. B--D-
2. B--C- 4. A--D-
A
B
?6 ?4 ?2 0
C 24
D
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)
Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the coordinates of the missing endpoint if P is the midpoint of -N-Q-.
7. N(2, 0), P(5, 2)
8. N(5, 4), P(6, 3)
9. Q(3, 9), P(-1, 5)
Use the number line to find the coordinate of the point the given fractional distance from A to B.
10. -16
11. -23
13. -34
14. -25
16. -13
17. -56
-3 -2 -1 0 1 2 3 4 5 6 7
12. -14 15. -15
Find P on N--M- that is the given fractional distance from N to M.
18. -23, N(-3, 1), M(2, 6)
19. -25, N(-2, 5), M(0, -4)
20. -14, N(-2, -1), M(8, 3)
21. -34, N(4, 5), M(-7, 1)
Refer to the graph at the right. 22. Find C on A-B- such that the ratio of AC to CB is 2:3. 23. Find C on A-B- such that the ratio of AC to CB is 1:3.
A
y 2
-4 -2 O -2 -4 -6
2 4x B
Chapter 1
20
Glencoe Geometry
P20-002A-890857
NAME
1-3 Practice
DATE
PERIOD
Locating Points and Midpoints
Use the number line to find the coordinate of the midpoint of each segment.
1. R--T 3. S--T
2. Q--R- 4. P-R-
P
Q
R
S
T
?10 ?8 ?6 ?4 ?2 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 D--F.
7. F(5, 8), E(4, 3)
8. F(2, 9), E(-1, 6)
9. D(-3, -8), E(1, -2)
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.
Use the number line to find the coordinate of the point the given fractional distance from A to B.
A
B
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
11. -13 15. -35
12. -15 16. -23
13. -16 17. -56
P21-1104801.. A--1434-890857
Find P on N--M- that is the given fractional distance from N to M.
19. -34, N(1, 7), M(9, -2) 21. -25, N(-3, -4), M(6, 3)
20. -45, N(-4, 5), M(2, -6) 22. -31, N(-4, 2), M(7, 9)
Refer to the graph at the right. 23. Find C on A-B- such that the ratio of AC to CB is 1:2.
24. Find C on A-B- such that the ratio of AC to CB is 4:3.
y
B
4
2
-4 -2 O -2
A
2 4x
Chapter 1
21
P21-002AG-l8en9c0o8e5G7eometry
Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-3
021_GEOCRMC01_715477.indd 21
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