Distance in Coordinate Geometry

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PRESENTATION

Chris is late for school and has quite the distance to go.

XX

Chris calls his dad Peter, who is watching TV.

By carOr by Plane

X

After politely asking his son why he was running late and reiterating the importance of a good education, Peter agrees to help get him there. The only question…

X0.5 mi

2.5 mi

“As the crow flies” – the shortest distance between two points.

Run

Rise

2.55 mi = c

Run

Rise

y2 – y1

A

AB2 = ( )2 + ( )2

B

x2 – x1

(1, -3)

(9, 9)

AB = 14.4

x2 – x1 y2 – y1

212

212 )()( yyxxAB

Distance from point A to B

A

B

(-5, -5)

(1, 3)

AB2 = ( a )2 + ( b )2x2 – x1 y2 – y1

Is the triangle GHI Scalene, Isosceles, or Equilateral??

G (2, 6) H (18, 2) I(12, 12)

( )2

212

212 )()( yyxxAB

Use the distance formula to write and equation for the circle.

212

212 )()( yyxxAB 2 3 3

Can we write the equation of a circle with center at (h,k) and radius r ?

2 29 ( 2) ( 3)x y

(x, y)

3(2, 3)

r

(x, y)

3(2, 3) (h, k)

2 2 2( ) ( )r x h y k

Radius squared

Equation of a Circle

2

(3, -2)

8

2 2 2( ) ( )r x h y k Equation of a Circle

2 2 28 ( 3) ( ( 2))x y

2 264 ( 3) ( 2)x y

/

(h, k)

r

Given the equation of the circle, find the center of the circle and the length of the radius.

x – (-3)13^2 = 169

2 2 2( ) ( )r x h y k Equation of a Circle

2 2169 ( 3) ( 4)x y

(h, k) = (-3, 4)

Assignment:

Pg 510, 1 - 12