1.1 Rectanglular Coordinates 2010 October 06, 2010
1.1 Rectangular Coordinates; Graphing Utilities
Objectives: Use the distance formula.
Use the midpoint formula.
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1.1 Rectanglular Coordinates 2010 October 06, 2010
The Distance Formula
y
y2
d
y1
y2 ­ y1
x2­ x1
x2
x1
x
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1.1 Rectanglular Coordinates 2010 October 06, 2010
The Distance Formula
y
y2
d
y1
y2 ­ y1
x 2­ x1
x1
x2
x
You can use the Pythagorean Theorem to find d.
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1.1 Rectanglular Coordinates 2010 October 06, 2010
The Distance Formula
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Find the distance d between the points (1, 3) and (5, 6).
2
2
d = (5 ­ 1) + ( 6 ­ 3) 2
2
d = (4) + (3) d = 16 + 9
d = 25
d = 5
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Consider the three points A = (­2, 1), B = (2, 3), and C = (3, 1).
a) Plot each point and form the triangle ABC.
B
A
C
Graph of triangle hiding behind graph!
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Consider the three points A = (­2, 1), B = (2, 3), and C = (3, 1).
b) Find the length of each side.
d(A, B) =
d(B, C) =
d(A, C) =
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Consider the three points A = (­2, 1), B = (2, 3), and C = (3, 1).
c) Verify that the triangle is a right triangle.
Use the Pythagorean Theorem to check.
Therefore, ABC is a right triangle.
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Consider the three points A = (­2, 1), B = (2, 3), and C = (3, 1).
d) Find the triangle's area.
B
A
Area = C
Because the right angle is at vertex B, the sides AB and BC form the base and height.
(Base)(Height)
square units
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Name the ordered pair of the midpoint between points A and B by looking at the graph.
8
midpoint
6
(3, 4)
4
2
­8
­6
­4
B
A
2
­2
4
6
8
­2
What formula could you
use if you don't have a graph but you know the ordered pairs for A and B?
­4
­6
­8
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1.1 Rectanglular Coordinates 2010 October 06, 2010
The Midpoint Formula
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Find the midpoint between the points (­15, 7) and (29, ­37).
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1.1 Rectanglular Coordinates 2010 October 06, 2010
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1.1 Rectanglular Coordinates 2010 October 06, 2010
Homework:
page 8
(15­21, 27­29, 33, 34, 39­44, 46­50, 60­63, 66­74)
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