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Name

LESSON

Date

Class

Practice A

Midpoint and Distance in the Coordinate Plane

1-6

Complete the statements. 1. A coordinate plane is a plane that is divided into four regions by a horizontal number line, the 2. The location, or Use the figure for Exercises 3­5. The midpoint of a segment has an x-coordinate that is the average of x1 x2 the x-coordinates of its endpoints ______ . The midpoint of a segment 2 has a y-coordinate that is the average of the y-coordinates of its y1 y2 endpoints ______ . 2 3. Q has coordinates (0, 0). R has coordinates (3, 0). _ Find the midpoint of QR .

_

, and a vertical number line, the , of a point are given by an ordered pair (x, y).

.

4. S has coordinates (0, 5. T has coordinates (3,

2). Find the midpoint of QS .

_

2). Find the midpoint of QT .

Use the figure for Exercises 6 and 7.

_

6. I is the midpoint of HJ . H has coordinates (0, 0), and I has coordinates ( 1, 2). Sketch these points in the coordinate plane. Study the graph and guess where _ J will be. Draw HJ . 7. Find the coordinates of J by using the Midpoint Formula. Use the figure for Exercises 8­12. Manuel is out for a jog. The thick lines on the grid are jogging paths. He is on his way home and is at D. His home is at E. Each unit on the grid is 1 mile. 8. Name the coordinates of D. 9. Find how many miles Manuel will jog if he goes straight to the x-axis. 10. Find how many miles Manuel will jog if he stays on the jogging paths all the way home. 11. Find how many miles Manuel will jog if he goes straight to the y-axis.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

43

Holt Geometry

LESSON

Practice A

Midpoint and Distance in the Coordinate Plane

LESSON

Practice B

Midpoint and Distance in the Coordinate Plane

1) and U(1, 6) and W(x 5) 2, y 3)

1-6

1-6

_

Complete the statements. 1. A coordinate plane is a plane that is divided into four regions by a horizontal number line, the 2. The location, or

Find the coordinates of the midpoint of each segment. 1. TU with endpoints T(5, .

_

(3, 2

3) 2

x-axis coordinates

, and a vertical number line, the

y-axis

2. VW with endpoints V( 2, , of a point are given by an ordered pair (x, y).

_

x y 3 __, _____ ( 4, 2)

3. Y is the midpoint of XZ. X has coordinates (2, 4), and Y has coordinates (­1, 1). Find the coordinates of Z. Use the figure for Exercises 4­7. 4. Find AB. 5. Find BC. 6. Find CA.

Use the figure for Exercises 3­5. The midpoint of a segment has an x-coordinate that is the average of x1 x 2 the x-coordinates of its endpoints ______ . The midpoint of a segment 2 has a y-coordinate that is the average of the y-coordinates of its y1 y2 endpoints ______ . 2 3. Q has coordinates (0, 0). R has coordinates (3, 0). _ Find the midpoint of QR .

_

26 units 26 units 4 2 units

_ _

1 1__, 0 2 (0, 1) 1 1__, 1 2

4. S has coordinates (0, 5. T has coordinates (3,

2). Find the midpoint of QS.

_

7. Name a pair of congruent segments. Find the distances.

AB and BC

2). Find the midpoint of QT .

Use the figure for Exercises 6 and 7.

_

6. I is the midpoint of HJ . H has coordinates (0, 0), and I has coordinates ( 1, 2). Sketch these points in the coordinate plane. Study the graph and guess where _ J will be. Draw HJ. 7. Find the coordinates of J by using the Midpoint Formula. Use the figure for Exercises 8­12. Manuel is out for a jog. The thick lines on the grid are jogging paths. He is on his way home and is at D. His home is at E. Each unit on the grid is 1 mile. 8. Name the coordinates of D. 9. Find how many miles Manuel will jog if he goes straight to the x-axis. 10. Find how many miles Manuel will jog if he stays on the jogging paths all the way home. 11. Find how many miles Manuel will jog if he goes straight to the y-axis.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

8. Use the Distance Formula to find the distance, to the nearest tenth, between K( 7, 4) and L( 2, 0). 9. Use the Pythagorean Theorem to find the distance, to the nearest tenth, between F(9, 5) and G(­2, 2).

6.4 units 11.4 units

( 2, 4)

Use the figure for Exercises 10 and 11. Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. The side pockets are halfway down the rails (long sides). 10. Find the distance, to the nearest tenth of a foot, diagonally across the table from corner pocket to corner pocket.

13.4 ft ( 1, 3)

11. Find the distance, to the nearest tenth of an inch, diagonally across the table from corner pocket to side pocket.

3 miles 4 miles 1 mile

Holt Geometry

101.8 in.

43

Copyright © by Holt, Rinehart and Winston. All rights reserved.

44

Holt Geometry

LESSON

Practice C

Midpoint and Distance in the Coordinate Plane

LESSON

Review for Mastery

Midpoint and Distance in the Coordinate Plane

1-6

1-6

1. When using the Distance Formula, the answer is the same regardless of which coordinates are designated (x1, y1) and (x 2, y 2). Demonstrate this fact by showing that (x1 x2)

2

2

(y1

y2)

2

(x2

x1)

2

(y2

2

y1) .

2

The midpoint of a line segment separates the segment into two halves. You can use the Midpoint Formula to find the midpoint of the segment with endpoints G(1, 2) and H(7, 6).

y

(x1

x1

2

x2)

(y1

x2

2

y2 )

y1

2

2

(x2

2y1y2 y2

x 1)

2

(y2

x2

2

y1) since

2x1x2 x1

2

2

x1 x2 y1 y2 M ______, ______ 2 2

2x1x2

y2

2

2y1y2

y1

2

_____ _____ M 1 7, 2 6 2 2 8 8 __, __ =M 2 2

7

H (7, 6)

M (4, 4) G (1, 2)

0 7 x

M is the midpoint _ of HG .

= M(4, 4) Visualize or sketch each situation. Find the answers without calculating. 2. The midpoint of a segment has coordinates (0, 0). One endpoint has coordinates (a, b). Find the coordinates of the other endpoint. 3. An endpoint of a segment has coordinates (0, 0). The midpoint has coordinates (d, e). Find the coordinates of the other endpoint. Use the figure for Exercises 4­7. 4. On the coordinate plane, plot points A( 3, 1), B(1, 3), C(2, _ and _ 1), _ D( 2, 1). Draw AB, AD, DC, _ and BC. Name the shape. 5. If each square on the grid represents one square meter, find the perimeter of ABCD to the nearest tenth of a meter. 6. Find the area of ABCD.

_

Find the coordinates of the midpoint of each segment. 1.

y 6

2.

B (4, 5)

3 x

y

S ( 3, 2) 3

x 0 3 3

( a,

b)

A ( 2, 5)

3

0

6

T (1,

4)

(2d, 2e) (1, 5)

_

( 1, (3, 6) (5, 0.5)

1)

3. QR with endpoints Q(0, 5) and R(6, 7)

_

4. JK with endpoints J(1, ­4) and K(9, 3)

rectangle 13.4 m 10 m2 11.7 m

_

Suppose M(3, 1) is the midpoint of CD and C has coordinates (1, 4). You can use the Midpoint Formula to find the coordinates of D. M (3, 1) x1 x2 y1 y2 M ______, ______ 2 2 y-coordinate of D Set the coordinates equal. Replace (x1, y1) with (1, 4). Multiply both sides by 2. Subtract to solve for x2 and y2. 6).

_

x-coordinate of D 3 3 6 5 x 1 x2 ______ 2 1 x2 ______ 2 1 x2 x2

7. Draw BD. Find the perimeter of triangle BCD to the nearest tenth of a meter.

1 1 2 6

8. Suki found a treasure map that was laid out on a grid. T had coordinates (3, 12), U had coordinates (7, 2), and V had coordinates (13, 13). Suki read the map's instructions: First, find the midpoint of segment UV, Or the treasure forever lost will be. Label this dreadful midpoint W, Or being well-off will never trouble you. W is in line with and between T and X, X! How clichéd! Can you guess what is next? TX is exactly two times TW, Be sure at X to bring a shovel or two.

y1 y2 ______ 2 4 y2 ______ 2 4 y2 y2

The coordinates of D are (5,

Name the coordinates where Suki found the treasure.

(17, 3)

5. M( 3, 2) is the midpoint of RS , and R has coordinates (6, 0). What are the coordinates of S?

_

( 12, 4) (15, 3)

Holt Geometry

6. M(7, 1) is the midpoint of WX , and X has coordinates ( 1, 5). What are the coordinates of W? Holt Geometry

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

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