Lesson 8.11 distance and midpoint formula Lesson 1-3: Formulas

Homework 1. P(-3,2) and R(5,3) 2. S(-4,-3) and T(5,10) Use the Distance Formula to find the distance of: 1. P(-3,2) and R(5,3) 2. S(-4,-3) and T(5,10) Use the Midpoint formula to find the midpoint between: 3. W(-4,4) and X(14,10) 4. B(11,-3) and D(-9,-4) Lesson 1-3: Formulas

The Distance Formula The distance d between any two points with coordinates and is given by the formula d = . Lesson 1-3: Formulas

Example 1: Finding Distances in the Coordinate Plane Use the Distance Formula to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5).

Example 1 Continued Use the Distance Formula. Substitute the values for the coordinates of D and E into the Distance Formula.

Example 2: Using the Distance Formula Find the length for FG and JK. Then determine whether FG  JK. Step 1 Find the coordinates of each point. F(1, 2), G(5, 5), J(–4, 0), K(–1, –3)

Example 2 Continued Step 2 Use the Distance Formula.

Check It Out! Example 3 Find EF and GH. Then determine if EF  GH. Step 1 Find the coordinates of each point. E(–2, 1), F(–5, 5), G(–1, –2), H(3, 1)

Check It Out! Example 3 Continued Step 2 Use the Distance Formula.

Example 4: Sports Application A player throws the ball from first base to a point located between third base and home plate and 10 feet from third base. What is the distance of the throw, to the nearest tenth?

Example 5 Continued Set up the field on a coordinate plane so that home plate H is at the origin, first base F has coordinates (90, 0), second base S has coordinates (90, 90), and third base T has coordinates (0, 90). The target point P of the throw has coordinates (0, 80). The distance of the throw is FP.

Midpoint Formula x1 = -2, x2 = 6, y1 = 5, and y2 = 4 In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are . Find the midpoint between (-2, 5) and (6, 4) Example: x1 = -2, x2 = 6, y1 = 5, and y2 = 4 M = M = Lesson 1-3: Formulas

Example 1: Finding the Coordinates of a Midpoint Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). = (–5, 5)

Check It Out! Example 1 Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

Circle Area: 𝐴=𝜋 𝑟 2 Circumference: C=𝜋2𝑟 or C=𝜋𝑑 Lesson 1-3: Formulas

Find the center of the circle Given a diameter with endpoints A(0,3) and B(5,1) Lesson 1-3: Formulas

Find the area of the circle Given a diameter with endpoints A(0,3) and B(5,1) Lesson 1-3: Formulas

Find the circumference of the circle Given a diameter with endpoints A(0,3) and B(5,1) Lesson 1-3: Formulas

Find the center, area, and circumference of the circle Given a diameter with endpoints F(-4,5) and E(-2,1) Lesson 1-3: Formulas