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Lesson 9.5-The Distance Formula HW:9.5/ 1-14

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Isosceles Right ∆Theorem 45° – 45° – 90° Triangle In a 45° – 45° – 90° triangle the hypotenuse is the square root of two * as long as each leg

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Theorem 30° – 60° – 90° Triangle In 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

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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 Material THE DISTANCE FORMULA

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Coordinate Geometry

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Coordinate Geometry - Investigation Use the Pythagorean Theorem to find the length of the segment 2 4 c 6 2

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Coordinate Geometry (AB) 2 = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The Distance Formula is based on the Pythagorean Theorem The distance between points A(x 1,y 1 ) and B(x 2,y 2 ) 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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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 hammer a.(-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 c

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b. Ferris Wheel and Hall of Mirrors (0, 0) and (3, 1) Using the points and Pythagorean theorem = DISTANCE FORMULA

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y Use the Pythagorean theorem 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) Using the points and Pythagorean theorem = DISTANCE FORMULA

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y Use the Pythagorean theorem d. Bumper Cars to Mime Tent (-4, -3) to (3, 3) x 7 6 c

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d. Bumper Cars to Mime Tent e. (-4, -3) to (3, 3)

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Exploration If 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? ≈2.46 Miles units *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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Find the distance between the points at (1, 2) and (–3, 0).

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Find the distance between the points at (2, 3) and (–4, 6).

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Find the distance between the points at (5, 4) and (0, –2).

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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?

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Homework Lesson 9.5 - Distance Formula 9.5/1-14

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Distance, Midpoint, Pythagorean Theorem. Distance Formula Distance formula—used to measure the distance between between two endpoints of a line segment.

Distance, Midpoint, Pythagorean Theorem. Distance Formula Distance formula—used to measure the distance between between two endpoints of a line segment.

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