Lesson 9.5-The Distance Formula
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Lesson 9.5-The Distance Formula
HW:9.5/ 1-14
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Isosceles Right ∆Theorem
2x
• 45° – 45° – 90° TriangleIn a 45° – 45° – 90° triangle the hypotenuse is the square root of two * as long as each leg
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Theorem
2
• 30° – 60° – 90° TriangleIn a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg
𝑥√3
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Problem Solving Strategy
Know the basic triangle rules
Solve for the other sides
Set known information equal to the corresponding part of the basic triangle
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New MaterialTHE DISTANCE FORMULA
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Coordinate Geometry
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Coordinate Geometry - InvestigationUse the Pythagorean Theorem to find the length of the segment
2
4
22 42 c
c 5220 c
47.4c 6
2
22 26 c
10240 c
32.6c
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Coordinate Geometry
(AB)2 = (x2 - x1)2 + (y2 - y1)2
The Distance Formula is based on the Pythagorean Theorem
The distance between points A(x1,y1) and B(x2,y2) is given by
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Coordinate Geometry - Example
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Exploration
• Get your supplies- Graph Paper- ruler- pencil
• Create a large XY coordinate grid
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Copy and label these points onto your graph paper, include the coordinates of each point
Exploration
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Exploration• Find the distance between the listed attractions• Use the Pythagorean theorem. • Draw right triangle if necessary.
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a. Bumper cars to sledge hammera. (-4, -3) to (2, -3)
x
y
Distance = 6
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b. Ferris Wheel and Hall of Mirrors(0, 0) and (3, 1)
x
y
3
1
Use the Pythagorean Theorem
=
=10
c
𝑐=√10𝑐 ≈3.16
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b. Ferris Wheel and Hall of Mirrors (0, 0) and (3, 1)
22 )10(30 22 )1()3(
16.310
𝑐=√𝑥2+𝑦 2
Using the points and Pythagorean theorem = DISTANCE FORMULA
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y Use the Pythagorean theorem
=
= 25
𝑐=√25𝑐=5
c. Refreshment Stand to Ball Toss(-5, 2) to (-2, -2)
x
3
4 c
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c. Refreshment Stand to Ball Toss (-5, 2) to (-2, -2)
22 )22(25 22 )4()3(
525
𝑐=√𝑥2+𝑦 2
Using the points and Pythagorean theorem = DISTANCE FORMULA
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y Use the Pythagorean theorem
=
=85
𝒄=√𝟖𝟓𝒄≈𝟗 .𝟐𝟐
d. Bumper Cars to Mime Tent(-4, -3) to (3, 3)
x
7
6c
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d. Bumper Cars to Mime Tente. (-4, -3) to (3, 3)
22 )33(34
22 )6()7(
22.985
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ExplorationIf your car is parked at the coordinates (17, -9),
and each grid unit represents 0.1 mile, how far is from your car to the refreshment stand?
22 29)5(17 d
22 )11(22 d
60.24605 d ≈2.46 Milesunits *0.1 miles
Try to complete this without plotting the location of your car.
Car to Refreshment stand(17, -9) to (-5, 2)
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22 02)3(1 d
22 24 d
20d
Find the distance between the points at (1, 2) and (–3, 0).
222
222 yyxxd
47.452
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22 63)4(2 d
22 )3(6 d
45d
Find the distance between the points at (2, 3) and (–4, 6).
71.653
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Find the distance between the points at (5, 4) and (0, –2).
√ ( 4+2 )2+ (5−0 )2
√ (6 )2+ (5 )2
√36+25
√61≈7.81
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Horseshoes Marcy is pitching a horseshoe in her local park. Her first pitch is 9 inches to the left and 3 inches below the pin. What is the distance between the horseshoe and the pin?
&
√¿¿¿√¿¿¿
√90
3√10≈9.49 𝑖𝑛
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Homework
Lesson 9.5 - Distance Formula9.5/1-14