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

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

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

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 Material THE DISTANCE FORMULA

Coordinate Geometry

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

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

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

Find the distance between the listed attractions Use the Pythagorean theorem. Draw right triangle if necessary.

a.Bumper cars to sledge hammer a.(-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 c

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

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

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

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

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)

Find the distance between the points at (1, 2) and (–3, 0).

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

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

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?

Homework Lesson Distance Formula 9.5/1-14