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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7/30/14 5:30 PM

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