warmup alg 2 16 april 2012
DESCRIPTION
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 Conic Sections. Section 9.1: Introduction to Conic Sections. What are Conic Sections?. Where are Conic Sections found?. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/1.jpg)
Warmup Alg 2 16 April 2012
![Page 2: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/2.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/3.jpg)
Section 9.1: Introduction to Conic Sections
![Page 4: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/4.jpg)
What are Conic Sections?
![Page 5: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/5.jpg)
Where are Conic Sections found?
The St. Louis Arch is an example of sort of a parabola.
![Page 6: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/6.jpg)
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!)
![Page 7: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/7.jpg)
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](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/8.jpg)
Where are Conic Sections found?
How many hyperbolas and circles here?
![Page 9: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/9.jpg)
The Conics
Circles
ParabolasHyperbolas
Ellipses
![Page 10: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/10.jpg)
Distance formulaFind the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436c10
![Page 11: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/11.jpg)
Distance formulaFind the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436c10
![Page 12: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/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
c6436c10
![Page 13: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/13.jpg)
The Distance FormulaTo 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
![Page 14: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/14.jpg)
The Midpoint FormulaThe 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
![Page 15: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/15.jpg)
The Midpoint FormulaTo say it another way:
Find the AVERAGE of the X’s and the AVERAGE of the Y’s!
2
,2
2121 yyxxM
![Page 16: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/16.jpg)
PracticeFind the distance between (-4, 2) and (-8, 4). Then find the midpoint between the points.
221
221 )()( yyxxD
22 )42()84( D22 )2()4( D
416 D
20D
2
,2
2121 yyxxM
242,
284M
26,
212M
3,6M
![Page 17: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/17.jpg)
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
![Page 18: Warmup Alg 2 16 April 2012](https://reader035.vdocuments.site/reader035/viewer/2022062410/56815f07550346895dcdc719/html5/thumbnails/18.jpg)
Assignment
Section 9.1: 6 – 14, 27 - 30