8/19/2019 Distance, Midpoint Formula,Circle Equation

1/2

DISTANCE FORMULA

Distance Formula – an equation that can be used to fnd the distance between any

pair o points on the coordinate plane.

d=√ ( X 2− X 1)

2+(Y 2−Y 

1)2

 

Vertical Distance (between two points) – the absolute value o the dierence o 

the y-coordinates o two points

ori!ontal Distance (between two points) - – the absolute value o the

dierence o the x-coordinates o two points

e.. Find the distance between ! "#$ -%& and ' "($ -%&

d= √ ( X 2− X 1)2+(Y 

2−Y 

1)2

d=  √ (9−4 )2+(−2−−2)2

d=  √ 25+0

d=  √ 25

d= 25units , horizontally aligned

MID"OINT FORMULA

)idpoint Formula – a ormula that can be used to fnd the coordinates o the

midpoint o a line sement on the coordinate plane

" X 

1+ X 

2

2,Y 

1+Y 

2

2 &

e.. Find the midpoint between ! "*$ +& and ' ",%$ ,&

" X 

1+ X 

2

2,Y 

1+Y 

2

2 &

"6+12

2,

8+10

2 &

"18

2,18

2 &

(   9 ,9 )

8/19/2019 Distance, Midpoint Formula,Circle Equation

2/2

STANDARD E#UATION OF A CIRCLE

 he /tandard 0quation o a 1ircle – the equation that defnes a circle with center at

"h$ 2& and a radius o r units.

"x-h&% 3 "y-2&%= r%

e..

x%3y%=#(  c="$& r=4 

"x-5&% 3 "y-*&% = +, "c=5$*&

 x y r 2

x=5 y=* r=(