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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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