Coordinate Algebra: Unit 6 Name___________________ Date_________________ Period________ Understanding & Applying the Distance Formula Guided Notes Standard and Skills MCC9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. SWBAT recognize the distance formula as a manipulation of the Pythagorean theorem SWBAT calculate the distance along a line by applying the distance formula SWBAT calculate the perimeter of a polygon by finding appropriate side lengths I. Pythagorean Theorem Example 1: Apply the Pythagorean Theorem (a2 + b2 = c2) to find the missing side length of each right triangle. Guided Practice Apply the Pythagorean Theorem (a2 + b2 = c2) to find the missing side length of each right triangle. Tell whether the side length you found is the hypotenuse or a leg. 1. a = 3, c = 5 2. a = 6, b = 8 3. b = 11, c = 12 4. 5. 6. II. The Distance Formula How to use the Pythagorean Theorem to determine the distance between two points on the coordinate plane: 1. 2. 3. 4. Draw a right triangle with the distance between the two points as the hypotenuse. Count the number of spaces along side a and side b. Write an equation in the form a2 + b2 = c 2 , plugging in the known values for a and b. Solve for length c, the distance between the two points. The Distance Formula When we solve for c, we have manipulated the Pythagorean theorem formula to become what we call ______________________. This formula is as follows: d= ( x2 x1 ) 2 ( y 2 y1 ) 2 Example: Find the distance between the two points given. Guided Practice Use either the Distance Formula or the Pythagorean theorem to find the distance between the two points. Independent Practice III. Calculating Perimeter Using the Distance Formula Perimeter: The _______________of all of the sides of a figure. Example: Finding the Perimeter of a figure by applying the distance formula Guided Practice 1. The vertices of triangle XYZ are listed below. X(-6, -5), Y(-10, -3), Z(-6, -3) What is the approximate perimeter of the triangle? A. 5.24 units B. 10.47 units C. 8.47 units D. 20.94 units 2. Given the triangle below, find the perimeter. Describe your reasoning.