September 16, 2018

1.9 Distance and Midpoint FormulasCirclesDeriving the distance formula: of tbh da

,

c

b

hypotenuse

Exited to'flat-

• -

T-0£

←

September 16, 2018

Distance Formula

The distance,

d,

between

( Xi, y , ) and ( Xz

, ya ) is

D= VT( Xz - X, ) 't Lys - y ,

)

September 16, 2018

D= ITGtb 't C- 2-45

= It

=y¥=yzf

← ←PerfFEEL

= IT - VBD=2473

September 16, 2018

To .

d-- E¥µµ2

- Tjd-

- Efts - an

d-- Et

d-- M¥4

d--

Ma.

I = 13

September 16, 2018

Midpoint FormulaThe midpoint of a

segment w/ endpoints a

(Xi, y , ) and Ck

, ya )a

is ( Xtzk , Yit⇒T

average of x - coordinates

September 16, 2018

( 1,2 ) ( 7,

- 3)

midpoint

( ' '

Ii E) ⇒ ( 4,

- I )

September 16, 2018

Circle

Definitionedacity

--

,

iA circle is the set of .

gona plane

•Iall pointseqantItalians

. .

.

from a fixed point i/

r

called the center, .

.

-r

→ the distance from thee

circle to the center

is the radius

September 16, 2018

Deriving an equation for a circle

# (h-xkF- I ( x - htt( y

- KT

f t •F- ( x - htt Cy - KJ

-

②ThestandardformoftheEquatimofac.ro#(x-h)2tCy-k)Z=r2

circle with center ( h,

k )radius =r

September 16, 2018

O=

CX-oft (y -05=22

X'ti:÷÷÷÷÷

.

September 16, 2018

September 16, 2018

How to graph a circle on a graphing calculator

Graphing a circle on Desmos

②X 't

y 2=4

*

4÷EI*u¥y = - VF

September 16, 2018

-

( Xt 2)'

t ( y - 3) 2=16

September 16, 2018

September 16, 2018

- C :C 2,

-4 )f- 3

September 16, 2018

September 16, 2018

The General Form of the Equation of a Circle

X'

t y2

t DX t Ey tf = O

1m÷T( x - htt Cy - k )

'= r

September 16, 2018

Converting from General to Standard Form

Ex. complete the squared )

D ( x'

t4xYty2-Gy23 grouping terms

L

→ (

x2t4xt4)t(y2-6yt9)=36

( Xtz ) 't ly -37=36 ¥543 )

September 16, 2018

Identify the center and radius of the circle