Objectives : Use the distance...
Transcript of Objectives : Use the distance...
![Page 1: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/1.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
Sep 119:58 AM
1.1 Rectangular Coordinates; Graphing Utilities
Objectives: Use the distance formula.Use the midpoint formula.
![Page 2: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/2.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
Sep 1110:02 AM
The Distance Formula
x
y
d
2x 1x
y2 1
yy2
1y
2x1x
![Page 3: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/3.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
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The Distance Formula
You can use the Pythagorean Theorem to find d.
x
y
d
2x 1x
y2 1yy2
1y
2x1x
![Page 4: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/4.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
Sep 113:14 PM
The Distance Formula
![Page 5: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/5.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
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Find the distance d between the points (1, 3) and (5, 6).
d = (5 1) + ( 6 3) 22
d = (4) + (3) 22
d = 16 + 9
d = 25d = 5
![Page 6: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/6.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
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A
B
C
Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).a) Plot each point and form the triangle ABC.
Graph of triangle hiding behind graph!
![Page 7: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/7.jpg)
1.1 Rectanglular Coordinates 2010
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Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).
b) Find the length of each side.
d(A, B) =
d(B, C) =
d(A, C) =
![Page 8: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/8.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
Sep 1110:02 AM
Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).
c) Verify that the triangle is a right triangle.
Use the Pythagorean Theorem to check.
Therefore, ABC is a right triangle.
![Page 9: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/9.jpg)
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d) Find the triangle's area.
Because the right angle is at vertex B, the sides AB and BC form the base and height.A
B
C
Area = (Base)(Height) square units
Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).
![Page 10: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/10.jpg)
1.1 Rectanglular Coordinates 2010
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Name the ordered pair of the midpoint between points A and B by looking at the graph.
midpoint
(3, 4)
What formula could youuse if you don't have a graph but you know the ordered pairs for A and B?
2
2
22
4
4
4
4
6
6 6
6
8
88
8
A
B
![Page 11: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/11.jpg)
1.1 Rectanglular Coordinates 2010
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October 06, 2010
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The Midpoint Formula
![Page 12: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/12.jpg)
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Find the midpoint between the points (15, 7) and (29, 37).
![Page 13: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/13.jpg)
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![Page 14: Objectives : Use the distance formula.staffweb.psdschools.org/kemotich/Mrs_Motichka/Precalculus... · 2010-10-06 · 1.1 Rectanglular Coordinates 2010 3 October 06, 2010 Sep 1110:02](https://reader030.fdocuments.us/reader030/viewer/2022040620/5f303065ebf34a722d27aa1f/html5/thumbnails/14.jpg)
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Homework:page 8
(1521, 2729, 33, 34, 3944, 4650, 6063, 6674)