Distance and Midpoints - Reyes' Math Classreyesmathclass.weebly.com/uploads/5/6/4/8/5648021/1-3_assignments… · Find the coordinates of the midpoint of a segment with the given

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Chapter 1 20 Glencoe Geometry

Skills PracticeDistance and Midpoints

Use the number line to find each measure.

1. LN 2. JL

3. KN 4. MN

Find the distance between each pair of points.

5.

x

y

O

F

G

6.

x

y

O

D

S

7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)

9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)

11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)

Use the number line to find the coordinate of the midpoint of each segment.

13. −−−

DE 14. −−−

BC

15. −−−

BD 16. −−−

AD

Find the coordinates of the midpoint of a segment with the given endpoints.

17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)

Find the coordinates of the missing endpoint if P is the midpoint of −−−

NQ .

19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)

–6 –4 –2 0 2 4 6 8 10 12

A B C D E

–6 –4 –2 0 2 4 6 8 10

J K L M N

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001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM

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PracticeDistance and Midpoints

Use the number line to find each measure.

1. VW 2. TV

3. ST 4. SV


5.

x

y

OM

Z 6.

x

y

O

E

S

7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)

9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)

Use the number line to find the coordinate of the midpoint of each segment.

11. −−

RT 12. −−−

QR

13. −−

ST 14. −−

PR


15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)

Find the coordinates of the missing endpoint if E is the midpoint of −−

DF .

17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)

20. 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.

–6 –4–10 –8 –2 0 2 4 6

P Q R S T

–6 –4–10 –8 –2 0 2 4 6 8

S T U V W

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Study Guide and InterventionDistance and Midpoints

Distance Between Two Points

Distance on a Number Line Distance in the Coordinate Plane

A B

x1

x2

AB = |x1 - x

2| or |x

2 - x

1|

Distance Formula: y

x

B(x2, y2)

A(x1, y1)

d = √ �� (x2 - x

1)2 + (y

2 - y

1)2

Use the number line to find AB.

AB = |(-4) - 2| = |- 6| = 6

-5 -4 -3 -2 -1 0 1 2 3

A B

Find the distance between A(-2, -1) and B(1, 3).Distance Formula

d = √ �� (x2 - x1)2 + ( y2 - y1)

2

AB = √ �� (1 - (-2))2+ (3 - (-1))2

AB = √ �� (3)2 + (4)2

= √ �� 25 = 5

ExercisesUse the number line to find each measure.

1. BD 2. DG

3. AF 4. EF

5. BG 6. AG

7. BE 8. DE


9. A(0, 0), B(6, 8) 10. R(-2, 3), S(3, 15)

11. M(1, -2), N(9, 13) 12. E(-12, 2), F(-9, 6)

13. X(0, 0), Y(15, 20) 14. O(-12, 0), P(-8, 3)

15. C(11, -12), D(6, 2) 16. K(-2, 10), L(-4, 3)

-10 -8 -6 -4 -2 0 2 4 6 8

A B C D E F G

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Example 1 Example 2


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Study Guide and Intervention (continued)

Distance and Midpoints

–10 –8 –6 –4 –2 0 2 4 6 8

A B C D E F G

-3 -2 -1 0 1 2

P Q

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Midpoint of a Segment

Midpoint on a Number Line

If the coordinates of the endpoints of a segment are x1 and x

2,

then the coordinate of the midpoint of the segment is x

1 + x

2 −

2 .

Midpoint on a

Coordinate Plane

If a segment has endpoints with coordinates (x1, y

1) and (x

2, y

2),

then the coordinates of the midpoint of the segment are ( x

1 + x

2 −

2 ,

y1 + y

2 −

2 ) .

Find the coordinate of the midpoint of −−

PQ .

The coordinates of P and Q are -3 and 1.

If M is the midpoint of −−−

PQ , then the coordinate of M is -3 + 1 − 2 = -2 −

2 or -1.

Find the coordinates of M, the midpoint of −−−

PQ , for P(-2, 4) and Q(4, 1).

M = ( x1+ x2 −

2 ,

y1+ y2 − 2 ) = (

-2 + 4 − 2 , 4 + 1 −

2 ) or (1, 2.5)

ExercisesUse 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


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)

Example 1

Example 2


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Word Problem PracticeDistance and Midpoints

1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?

y

xO

Cabins

Mess Hall

2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?

3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?

y

xO

4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.

5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.

y

xO

Ben’s House

Kate’s House

a. How many yards apart are Kate’s and Ben’s homes?

b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.

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Distance and Midpoints - Reyes' Math Classreyesmathclass.weebly.com/uploads/5/6/4/8/5648021/1-3_assignments… · Find the coordinates of the midpoint of a segment with the given