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

2. 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

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

4. 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).

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

6. 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)

7. Example 2 Continued
Step 2 Use the Distance Formula.

8. 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)

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

10. 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?

11. 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.

12. 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

13. 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)

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

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

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

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

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

19. 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