Download Midpoint and Distance in the Coordinate Plane

1-7
PART 1
Midpoint and Distance
in the Coordinate Plane
Vocabulary
Review
Use the figure at the right for Exercises 1–6. Write T for true or F for false.
1. A segment has two endpoints.
4
A
y
B
2
2. A segment is named with two arrowheads.
* )
Ľ2
Ľ4
3. AB is a segment of AB .
x
C
D
2
4
Ľ2
4. The segment with endpoints B and C can only be named BC.
Ľ4
5. BD is on the y-axis.
Vocabulary Builder
midpoint (noun)
MID
poynt
Definition: A midpoint of a segment is a point that divides the segment into two
congruent segments.
Use Your Vocabulary
y
Use the figure at the right for Exercises 7–9.
7. The midpoint of EF is G(
8. The midpoint of AB is (
,
,
4
).
C
), or the origin.
Ľ4
9. The midpoint of CD is (
,
).
D
O
Ľ2
A
52
B
G
E
Ľ4
Chapter 1
F
2
x
4
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
6. Two opposite rays form a segment.
Key Concept Midpoint Formulas
On a Number Line
In the Coordinate Plane
The coordinate of the midpoint M of AB
a àb
.
with endpoints at a and b is
2
Given A(x1, y1) and B(x2, y2), the coordinates of the
x1 àx2 y1 ày2
.
,
midpoint of AB are M
2
2
(
)
10. How do you know when to use each midpoint formula?
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11. Complete the diagram below.
4
2
y
(17, 4)
(,)
(1, 2)
O
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
(à4) ó2
(1 à) ó2
x
2
4
6
8
10
12
14
16
Problem 1 Finding the Midpoint
Got It? JK has endpoints at 212 and 4 on a number line. What is the coordinate
of its midpoint?
12. Circle the formula you will use.
a1b
2
a2b
2
Ma
x1 1 x2 y1 1 y2
2
,
2
b
Ma
x1 2 x2 y1 2 y2
2
,
2
b
13. Find the coordinate of the midpoint.
14. Label points J and K and their coordinates and graph the midpoint on the number
line below.
214
210
28
26
24
22
0
53
2
6
Lesson 1-7, Part 1
Problem 2 Finding an Endpoint
Got It? The midpoint of AB has coordinates (4, 29). Endpoint A has coordinates
(23, 25). What are the coordinates of B?
15. Circle the correct description of the coordinates of the given points.
ordered pairs
real numbers
16. Complete the equations below.
(
)
,
x1 1
y1 1
,
2
2
)
x1 1
(
,
)
y1 1
2
5
x1 1
5
2
5
y1 1
5
← Solve two equations. →
x1 5
y1 5
17. The coordinates of endpoint B are (
,
).
Lesson Check • Do you UNDERSTAND?
Error Analysis XY has endpoints at 23 and 7. Shelby calculates the midpoint of
XY . What is her error?
18. Circle the correct description of the coordinates of the given endpoints.
ordered pairs
real numbers
19. Underline the correct word to complete the sentence.
The coordinate of the midpoint is the average / difference of the coordinates of
the endpoints.
20. Draw XY on the number line below.
24 23 22 21
0
1
2
3
4
5
6
7
8
9 10
21. What is the error?
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Chapter 1
54
M = -3 - 7
2
= -5
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
(
Midpoint Coordinates
Midpoint Formula
Endpoint A Coordinates