warmup alg 2 16 april 2012

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 formulaFind the missing side of the triangle.

6

8

a2 + b2 = c2

62 + 82 = c2

c 22 86

c6436c10

Distance formulaFind the missing side of the triangle.

6

8

a2 + b2 = c2

62 + 82 = c2

c 22 86

c6436c10

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

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

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

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

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

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