5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

Lesson 11-5 The Distance Formula

Transparency 5 Click the mouse button or press the Space Bar to display the answers.

Transparency 5a

Objectives Find the distance between two points on the coordinate plane Find a point that is a given distance from a second point in a plane

Vocabulary None new

Distance ConceptFormulaExamples Nr line Coord Plane D = | a – b |D = | 2 – 8| = 6 D = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 D = (7-1) 2 + (4-2) 2 = 40 a b (1,2) (7,4) Y X ∆x∆x ∆y∆y D ∆y = y 2 – y 1 ∆x = x 2 – x 1 D 2 = ∆x 2 + ∆y 2 Application of Pythagorean Theorem

Example 1 Find the distance between the points at (1, 2) and (–3, 0). Answer:or about 4.47 units Distance Formula and Simplify. Evaluate squares and simplify

Example 2 Biathlon Julianne is sighting her rifle for an upcoming biathlon competition. Her first shot is 2 inches to the right and 7 inches below the bull’s-eye. What is the distance between the bull’s-eye and where her first shot hit the target? Draw a model of the situation on a coordinate grid. If the bull’s-eye is at (0, 0), then the location of the first shot is (2, –7). Use the Distance Formula.

Example 2 cont Distance Formula or about 7.28 inches Answer: The distance isor about 7.28 inches.

Example 3 Find the value of a if the distance between the points at (2, –1) and (a, –4) is 5 units. Distance Formula Simplify. Evaluate squares.Simplify. Let and.

Example 3 cont Square each side. Subtract 25 from each side. Factor. Solve. Answer: The value of a is –2 or 6. Zero Product Property or

Summary & Homework Summary: –The distance d between any two points with coordinates (x 1, y 1 ) and (x 2, y 2 ) is given by d = √(x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 –It is an application of the Pythagorean theorem Homework: –pg