Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro...
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Transcript of Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro...
![Page 1: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/1.jpg)
Warmup Alg 2 16 April 2012
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Agenda• Don't forget about resources on
mrwaddell.net
• Section 9.1: Intro to Conic Sections• Distance and midpoint formula• Recognizing Conic Sections
![Page 3: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/3.jpg)
Section 9.1: Introduction to Conic Sections
![Page 4: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/4.jpg)
What are Conic Sections?
![Page 5: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/5.jpg)
Where are Conic Sections found?
The St. Louis Arch is an example of sort of a parabola.
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Where are Conic Sections found?
Ferris wheels are circular. They were also invented by George Ferris, who lived in Carson City for a while (and whose father was a founder of Knox College where I went to college!)
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Where are Conic Sections found?
St. Paul’s Cathedral, the Washington Capitol and the Mormon Tabernacle Choir are all Ellipses.
If you are at one foci, you can hear what is happening at the other.
![Page 8: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/8.jpg)
Where are Conic Sections found?
How many hyperbolas and circles here?
![Page 9: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/9.jpg)
The Conics
Circles
ParabolasHyperbolas
Ellipses
![Page 10: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/10.jpg)
Distance formula
Find the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436
c10
![Page 11: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/11.jpg)
Distance formulaFind the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436
c10
![Page 12: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/12.jpg)
Distance formulaFind the distance in RED
(-2,7)
(4,-1)
a2 + b2 = c2
(4- -2)2 + (-1- 7)2 = c2
c 22 )8(6
c6436
c10
![Page 13: Warmup Alg 2 16 April 2012. Agenda Don't forget about resources on mrwaddell.net Section 9.1: Intro to Conic Sections Distance and midpoint formula Recognizing.](https://reader031.fdocuments.net/reader031/viewer/2022032803/56649e405503460f94b3224d/html5/thumbnails/13.jpg)
The Distance Formula
To find the distance between any two points (x1, y1) and (x2, y2), use the distance formula:
Distance =
Hmm, kind of looks like the Pythagorean Theorem!
221
221 )()( yyxx
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The Midpoint Formula
The midpoint of a line is halfway between the two endpoints of a line.
To find the midpoint between (x1, y1) and (x2, y2), , use the midpoint formula:
2
,2
2121 yyxxM
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The Midpoint Formula
To say it another way:
Find the AVERAGE of the X’s and the AVERAGE of the Y’s!
2
,2
2121 yyxxM
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PracticeFind the distance between (-4, 2) and (-8, 4). Then find the midpoint between the points.
221
221 )()( yyxxD
22 )42()84( D
22 )2()4( D
416 D
20D
2
,2
2121 yyxxM
2
42,
2
84M
2
6,
2
12M
3,6M
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Classify a Triangle using the Distance formula
If a triangle has:
3 sides the same:
2 side the same:
No sides the same:
Then it is:
Equilateral
Isoceles
Scalene
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Assignment
Section 9.1: 6 – 14, 27 - 30