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Lesson 9.5-The Distance Formula
HW:9.5/ 1-14
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
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
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
New MaterialTHE DISTANCE FORMULA
Coordinate Geometry
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
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
Coordinate Geometry - Example
Exploration
• Get your supplies- Graph Paper- ruler- pencil
• Create a large XY coordinate grid
Copy and label these points onto your graph paper, include the coordinates of each point
Exploration
Exploration• Find the distance between the listed attractions• Use the Pythagorean theorem. • Draw right triangle if necessary.
a. Bumper cars to sledge hammera. (-4, -3) to (2, -3)
x
y
Distance = 6
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
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
y Use the Pythagorean theorem
=
= 25
𝑐=√25𝑐=5
c. Refreshment Stand to Ball Toss(-5, 2) to (-2, -2)
x
3
4 c
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
y Use the Pythagorean theorem
=
=85
𝒄=√𝟖𝟓𝒄≈𝟗 .𝟐𝟐
d. Bumper Cars to Mime Tent(-4, -3) to (3, 3)
x
7
6c
d. Bumper Cars to Mime Tente. (-4, -3) to (3, 3)
22 )33(34
22 )6()7(
22.985
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)
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
22 63)4(2 d
22 )3(6 d
45d
Find the distance between the points at (2, 3) and (–4, 6).
71.653
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
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
Homework
Lesson 9.5 - Distance Formula9.5/1-14