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Lesson Menu Five-Minute Check (over Lesson 10–4) Then/Now New Vocabulary Key Concept: Distance Formula Example 1: Find the Distance Between TwoExample 1: Find the Distance Between Two PointsPoints Example 2: Real-World Example: Use the Distance Formula Concept Summary: Formulas Example 3: Find the Perimeter

Over Lesson 10–4 5-Minute Check 1 A.c = 16 B.c = 17 C.c = 18 D.c = 20 What is the length of the hypotenuse of a right triangle with sides a = 8 and b = 15?

Over Lesson 10–4 5-Minute Check 2 A.c = 13.1 B.c = 13.2 C. c = 13.3 D.c = 13.4 What is the length of the hypotenuse of a right triangle with sides a = 6 and b = 12?

Over Lesson 10–4 5-Minute Check 3 A.yes B.no The lengths of three sides of a triangle are given. Determine whether the triangle is a right triangle. a = 7 b = 24 c = 25

Over Lesson 10–4 5-Minute Check 4 A.yes B.no The lengths of three sides of a triangle are given. Determine whether the triangle is a right triangle. a = 10 b = 12 c = 15

Over Lesson 10–4 5-Minute Check 5 A.8.8 in. B.8.7 in. C.8.6 in. D.8.5 in. A computer screen has a diagonal of 14 inches. The width of the screen is 11 inches. Find the height of the screen.

Then/Now You found the slope of a line passing through two points on a coordinate plane. (Lesson 8–6) Use the Distance Formula to find the distance between two points on a coordinate plane. Apply the Distance Formula to solve problems about figures on the coordinate plane.

Vocabulary Distance Formula

Concept A

Example 1 Find the Distance Between Two Points Find the distance between M(8, 4) and N(–6, –2). Round to the nearest tenth, if necessary. Use the Distance Formula. Distance Formula (x 1, y 1 ) = (8, 4), (x 2, y 2 ) = (–6, –2) Simplify. Evaluate (–14) 2 and (–6) 2.

Example 1 Find the Distance Between Two Points Add 196 and 36. Answer: The distance between points M and N is about 15.2 units. Take the square root.

Example 1 A.4.1 units B.8.1 units C.14.0 units D.15.7 units Find the distance between A(–4, 5) and B(3, –9). Round to the nearest tenth, if necessary.

Example 2 Use the Distance Formula SOCCER Javy kicks a ball from a position that is 2 yards behind the goal line and 4 yards from the sideline (–2, 4). The ball lands 8 yards past the goal line and 2 yards from the same sideline (8, 2). What distance, to the nearest tenth, was the ball kicked?

Example 2 Use the Distance Formula Distance Formula (x 1, y 1 ) = (–2, 4) (x 2, y 2 ) = (8, 2) Understand You know the coordinates of the two locations and that each unit represents 1 yard. You need to find the distance between the two points. Plan Use the Distance Formula to find the distance the ball was kicked. Solve

Example 2 Use the Distance Formula d ≈ 10.2 Answer: Javy kicked the ball 10.2 yards Simplify. Evaluate powers. Simplify. Check The distance is slightly greater than 10 yards, so the answer is reasonable. 

Example 2 A.0.2 mi B.0.5 mi C.2.2 mi D.5 mi MAPS The map of a college campus shows Gilmer Hall at (7, 3) and Watson House dormitory at (5, 4). If each unit on the map represents 0.1 mile, what is the distance between these buildings?

Concept B

Example 3 Find the Perimeter Step 1 Use the Distance Formula to find the length of each side of the triangle. GEOMETRY Classify ΔXYZ by its sides. Then find its perimeter to the nearest tenth.

Example 3 Find the Perimeter Distance Formula (x 1, y 1 ) = (–5, 1), (x 2, y 2 ) = (–2, 4) Side XY: X(–5, 1), Y(–2, 4) Simplify. Evaluate powers. Simplify.

Example 3 Find the Perimeter Side YZ: Y(–2, 4), Z(–3, –3) Distance Formula (x 1, y 1 ) = (–2, 4), (x 2, y 2 ) = (–3, –3) Simplify. Evaluate powers. Simplify.

Example 3 Find the Perimeter Side ZX: Z(–3, –3), X(–5, 1) Distance Formula (x 1, y 1 ) = (–3, –3), (x 2, y 2 ) = (–5, 1) Simplify. Evaluate powers. Simplify.

Example 3 Find the Perimeter Step 2 Add the lengths of the sides to find the perimeter. Answer: The triangle is scalene. The perimeter is about 15.8 units. None of the sides are congruent. So, ΔXYZ is scalene.

Example 3 A.21.3 units B.14.6 units C.13.4 units D.10.9 units GEOMETRY Find the perimeter of ΔXYZ to the nearest tenth.

End of the Lesson