9.1 Distance and Midpoint Formulas

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

x

y

(-3,-5)

(7,2)

The Distance Formula:

To calculate the distance between the points and

Visually, you are using the Pythagorean Theorem to determine a hypotenuse.

The Midpoint Formula:

To determine the midpoint of any line segment joining and

Take the mean of the x values and take the mean of the y values. THESE ARE COORDINATES OF A POINT

Examples:

2.14.13Tuesday, July 17, 201210:26 PM

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Examples:

Find the distance between and

Find the midpoint of the line segment joining (4, 1) and (1, -5)

Find an equation for the perpendicular bisector of for the points A(3, 5) and B(9, -3). Let P(x, y) be any point on the perpendicular bisector.

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Practice:

Calculate the distance and the midpoint for each pair of points.

(-3, -1), (-7, -5)

(.5, 0), (3, -6)

,

9.2 Circles

Vocabulary

Conic sections (conics): plane curves having second-degree equations. Obtained by slicing a double cone with a plane.

•

Circle: all the points in a plane that are a fixed distance from a fixed point.•

Radius: fixed distance of a circle•

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Radius: fixed distance of a circle•

Center: the fixed point of a circle•

Translation: sliding a graph to a new position in the coordinate plane without changing its shape

•

Equation of a Circle

The circle with center (h, k) and radius r has the equation

Examples:

Find an equation of the circle with center (3, -4) and radius 6

x

y

Graph:

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Find the center and radius of the circle

x

y

x

y

The center of a circle of radius 5 lies in the first quadrant. Find an equation of the circle if it is tangent to the x-axis at (1, 0).

Practice:

Find an equation of the circle with center (-1, 3) and radius 2

x

y

Graph

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x

y

If the graph of the given equation is a circle, find its center and radius; if the equation has no graph, say so.

x

y

p. 410-11 #7, 11, 17, 27-31 odd, 37-41 odd, 47In Class: p. 404-05 #11-15 odd, 21, 25, 27

Homework: MathXL 9.1-2HW

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Homework: MathXL 9.1-2HW

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