1-7 Midpoint and Distance in the Coordinate...
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Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Vocabulary Review x y O 4 4 2 4 4 B A C G D E F C E F A D B x y 8 5 10 Chapter 1 26 Midpoint and Distance in the Coordinate Plane 1-7 Use the figure at the right for Exercises 1–6. Write T for true or F for false. 1. Points A and B are both at the origin. 2. If AB 5 BC , then B is the midpoint of AC . 3. The midpoint of AE is F. 4. The Pythagorean Theorem can be used for any triangle. 5. Point C is at (6, 0). 6. Point E has a y-coordinate of 28. 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 Use the figure at the right for Exercises 7–9. 7. The midpoint of EF is G( , ). 8. The midpoint of AB is ( , ), or the origin. 9. The midpoint of CD is ( , ).
Transcript of 1-7 Midpoint and Distance in the Coordinate...
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Chapter 1 26
Midpoint and Distance in the Coordinate Plane1-7
Use the figure at the right for Exercises 1–6. Write T for true or F for false.
1. Points A and B are both at the origin.
2. If AB 5 BC , then B is the midpoint of AC .
3. The midpoint of AE is F.
4. The Pythagorean Theorem can be used for any triangle.
5. Point C is at (6, 0).
6. Point E has a y-coordinate of 28.
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
Use the figure at the right for Exercises 7–9.
7. The midpoint of EF is G( , ).
8. The midpoint of AB is ( , ), or the origin.
9. The midpoint of CD is ( , ).
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d.Key Concept Midpoint Formulas
Problem 2
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(17, 4)
( 4) 2
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On a Number Line In the Coordinate Plane
Given A(x1, y1) and B(x2, y2), the coordinates of the
( ,x1 x2
2 )y1 y2
2midpoint of AB are M
The coordinate of the midpoint M of AB
.a b
2with endpoints at a and b is
Midpoint Formula Midpoint Coordinates
,( )x1 1
2
y1 1
2,
y1 1
25
y1 1 5
y1 5
x1 1
25
x1 1 5
x1 5
← Solve two equations. →
( , )
Endpoint A Coordinates
( )
27 Lesson 1-7
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. Complete the equations below.
16. The coordinates of endpoint B are ( ).
Find the coordinate of the midpoint M of each segment with the given endpoints on a number line.
10. endpoints 5 and 9 11. endpoints 23 and 5
12. endpoints 210 and 23 13. endpoints 28 and 21
14. Complete the diagram below.
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Problem 3
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y2 y1
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S(–2, 14)
R(3, –1)
Chapter 1 28
Finding Distance
Got It? SR has endpoints S(22, 14) and R(3, 21). What is SR to the nearest tenth?
20. Complete the diagram at the right.
21. Let S(22, 14) be (x1, y1) and let R(3, 21) be (x2, y2) . Use the justifications and complete thesteps below to find SR.
d 5 ÄQ 2 x1R2 1 Q 2 y1R2 Use the Distance Formula.
SR 5 ÄQ 2 (22)R2 1 Q 2 14R2 Substitute.
5 ÄQ R2 1 Q R2 Subtract.
5 Ä 1
Simplify powers.
5 Ä Add.
< Use a calculator.
Formula The Distance Formula
Use the diagrams above. Draw a line from each triangle side in Column A to the corresponding triangle side in Column B.
Column A Column B
17. y2 2 y1 a
18. x2 2 x1 b
19. distance, d c
Th e distance between two points A(x1, y1) and B(x2, y2) is d 5 "(x2 2 x1)2 1 (y2 2 y1)2.
Th e Distance Formula is based on the Pythagorean Th eorem.
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d.Problem 4
Math Success
Lesson Check
Now Iget it!
Need toreview
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29 Lesson 1-7
Finding Distance
Got It? On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform A and zip to each of the other platforms. How far do you travel from Platform D to Platform E? Each grid unit represents 5 m.
22. The equation is solved below. Write a justification for each step.
d 5 "(x2 2 x1)2 1 (y2 2 y1)2
DE 5 "(30 2 20)2 1 (215 2 20)2
5 "102 1 (235)2 5 "100 1 1225 5 "1325
23. To the nearest tenth, you travel about m.
Reasoning How does the Distance Formula ensure that the distance between two diff erent points is positive?
24. A radical symbol with no sign in front of it indicates a positive / negative square root.
25. Now answer the question.
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midpoint distance coordinate plane
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