The document discusses distance and midpoint formulas as well as circles. It provides examples of finding the distance between two points, finding the midpoint of a line segment between two points, writing the standard form equation of a circle given its center and radius, and finding the center and radius of a circle given its equation in general form. It also discusses graphing circle equations and identifying the domain and range from the graph.

1. Section 2.8 Distance and Midpoint Formulas; Circles

2. The Distance Formula

5. Example Find the distance between (4,-5) and (9,-2).

6. The Midpoint Formula

7. (-1,5) (6,8)

8. Example Find the midpoint of the segment whose endpoints are (-1,7) and (-5,9).

9. Circles

11. Graphing Calculator

12. Write the standard form of the equation of the circle with center (-4,1) and radius of 3. Standard Form (-4,1) 3

13. Find the center and radius of the circle whose equation is Graph the equation. Use the graph to identify the relation’s domain and range. Why is it a relation and not a function? 3 (-3,4) Domain: [-6,0]; Range:[1,7] Center(-3,4); radius=3

14. Example Write the standard form of the equation of the circle with center at (-2,7) and a radius of 5.

15. Example Find the center and radius of the circle whose equation is below. Graph the equation. Use the graph to identify the relation’s domain and range.

16. General Form

17. ? ?

18. Example Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

19. Example Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

20. (a) (b) (c) (d) Find the distance between the points (-1,8) and (9,5).

21. (a) (b) (c) (d) Find the midpoint of the line segment with the endpoints of (-1,-1) and (- 5,8).

22. (a) (b) (c) (d) Write the equation of the line with center at (0,7) and a radius of 4.