Distance Formula Mr. Peter Richard will go the distance to teach you this very far out lesson! Objectives: Find distance between two points in the coordinate plane 10 miles Wow, that plane is really far out from the airport!

Recall the Pythagorean Theorem c2 = a2 + b2 a and b are the legs c is the hypotenuse (the longest length) only applies to right triangles

Relate Distance Formula to the Pythagorean Theorem c2 = a2 + b2

Use the Distance Formula to find the distance between points F and G, to the nearest tenth. Write the distance formula. Substitute in known values. Simplify the Equation

Using the Distance Formula Try It! Using the Distance Formula Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth. Use the distance formula Substitute Simplify Simplify Simplify

Real-world and the Distance Formula You are building a fence to enclose an area as shown in the diagram. Approximately, how many feet of fencing will be required? EF = FG = GH = HE = The approximate amount of fencing needed (perimeter) is 5.4 + 5.1 + 5 + 7.1 = 22.6 feet.

Check It Out! The center of the pitching mound has coordinates (42.8, 42.8). When a pitcher throws the ball from the center of the mound to home plate, what is the distance of the throw, to the nearest tenth?  60.5 ft

DO NOW Classwork: The Distance Formula 1. Find the distance between the endpoints M(2, –1) and N(–4, 3) to the nearest tenth. 2. Find the distance between P(–2.5, 3.5) and R(–7.5, 8.5) to the nearest tenth. 3. Find the distance, to the nearest tenth, between S(6, 5) and T(–3, –4). 4. Find the length of CD, C(6, –4) and D(12, –2). The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1), and C(–4, –2). Find the perimeter of ∆ABC, to the nearest tenth. Draw out on a graph to help you out if you want! Homework: Page 186 # 51-55

Lesson Quiz: Part I 1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0). (3, 3) 2. K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L. (17, 13) 3. Find the distance, to the nearest tenth, between S(6, 5) and T(–3, –4). 12.7 4. The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1), and C(–4, –2). Find the perimeter of ∆ABC, to the nearest tenth. 26.5