Math 71 10.1 – Distance and Midpoint Formulas; Circles 1
Jan 19, 2016
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