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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?
The St. Louis Arch is an example of sort of a parabola.
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!)
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.
Where are Conic Sections found?
How many hyperbolas and circles here?
The Conics
Circles
ParabolasHyperbolas
Ellipses
Distance formula
Find the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436
c10
Distance formulaFind the missing side of the triangle.
6
8
a2 + b2 = c2
62 + 82 = c2
c 22 86
c6436
c10
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
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
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
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
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
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
Assignment
Section 9.1: 6 – 14, 27 - 30