1

Math 71

10.1 – Distance and Midpoint Formulas; Circles

2

The Distance Formula

Can use Pythagorean Theorem to get the distance formula:

Suppose you’re looking for the distance from point at to point at .

3

Ex 1.Find the distance between and .

The Distance Formula

4

The Midpoint Formula

Midpoint formula:

Ex 2.Find the midpoint of the segment with endpoints and .

5

The Midpoint Formula

Midpoint formula:

Ex 2.Find the midpoint of the segment with endpoints and .

6

The Midpoint Formula

Midpoint formula:

Ex 2.Find the midpoint of the segment with endpoints and .

7

The Midpoint Formula

Midpoint formula:

Ex 2.Find the midpoint of the segment with endpoints and .

8

A circle is the set of all points a given distance (__________) from a given point (__________).

Circles

9

A circle is the set of all points a given distance (__________) from a given point (__________).

Circles

radius

10

A circle is the set of all points a given distance (__________) from a given point (__________).

Circles

radius center

11

Squaring both sides, we get the standard form of the equation of a circle with center and radius :

Circles

What’s the distance from the center to any point on the circle ?

12

Squaring both sides, we get the standard form of the equation of a circle with center and radius :

Circles

What’s the distance from the center to any point on the circle ?

13

Squaring both sides, we get the standard form of the equation of a circle with center and radius :

Circles

What’s the distance from the center to any point on the circle ?

14

Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.

Circles

15

Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.

Circles

16

Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.

Circles

17

Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.

Circles

18

Ex 4.Find the center and radius of the circle whose equation is , and graph it.

Circles

19

Ex 4.Find the center and radius of the circle whose equation is , and graph it.

Circles

20

Ex 4.Find the center and radius of the circle whose equation is , and graph it.

Circles

21

Ex 4.Find the center and radius of the circle whose equation is , and graph it.

Circles

22

The general form of the equation of a circle is

We can convert from general form to standard form by ________________________.

Ex 5.Write in standard form:

Circles

23

The general form of the equation of a circle is

We can convert from general form to standard form by ________________________.

Ex 5.Write in standard form:

Circles

completing the square

24

The general form of the equation of a circle is

We can convert from general form to standard form by ________________________.

Ex 5.Write in standard form:

Circles

completing the square