1-3 Study Guide and Intervention
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
mx - x
2 1 + − . n
(
mx2 - x1
my2 - 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
mx 2 - x 1
my 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
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
mx - x
2 1 + − . n
(
mx2 - x1
my2 - 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
mx 2 - x 1
my 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
