objectives : use the distance...
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1.1 Rectanglular Coordinates 2010
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1.1 Rectangular Coordinates; Graphing Utilities
Objectives: Use the distance formula.Use the midpoint formula.
1.1 Rectanglular Coordinates 2010
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The Distance Formula
x
y
d
2x 1x
y2 1
yy2
1y
2x1x
1.1 Rectanglular Coordinates 2010
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The Distance Formula
You can use the Pythagorean Theorem to find d.
x
y
d
2x 1x
y2 1yy2
1y
2x1x
1.1 Rectanglular Coordinates 2010
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The Distance Formula
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Find the distance d between the points (1, 3) and (5, 6).
d = (5 1) + ( 6 3) 22
d = (4) + (3) 22
d = 16 + 9
d = 25d = 5
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A
B
C
Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).a) Plot each point and form the triangle ABC.
Graph of triangle hiding behind graph!
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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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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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d) Find the triangle's area.
Because the right angle is at vertex B, the sides AB and BC form the base and height.A
B
C
Area = (Base)(Height) square units
Consider the three points A = (2, 1), B = (2, 3), and C = (3, 1).
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Name the ordered pair of the midpoint between points A and B by looking at the graph.
midpoint
(3, 4)
What formula could youuse if you don't have a graph but you know the ordered pairs for A and B?
2
2
22
4
4
4
4
6
6 6
6
8
88
8
A
B
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The Midpoint Formula
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Find the midpoint between the points (15, 7) and (29, 37).
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Homework:page 8
(1521, 2729, 33, 34, 3944, 4650, 6063, 6674)