Chapter 1.9 Preparatory math class University

1.9 precalculus

1. Copyright © Cengage Learning. All rights reserved.
1.9
The Coordinate Plane;
Graphs of Equations; Circles

2. 2
Objectives
■The Coordinate Plane
■The Distance and Midpoint Formulas
■Graphs of Equations in Two Variables
■Intercepts
■Circles
■Symmetry

3. 3
The Coordinate Plane

4. 4
The Distance and Midpoint
Formulas

5. 5
The Distance and Midpoint Formulas
Figure 4

6. 6
The Distance and Midpoint Formulas

7. 7
Example 2 –Applying the Distance Formula
Which of the points P (1, –2) or Q(8, 9) is closer to the point
A(5, 3)?
Solution:
By the Distance Formula we have

8. 8
The Distance and Midpoint Formulas

9. 9
Graphs of Equations in
Two Variables

10. 10
Intercepts

11. 11
Intercepts
The x-coordinates of the points where a graph intersects
the x-axis are called the x -intercepts of the graph and are
obtained by setting y = 0 in the equation of the graph.
The y-coordinates of the points where a graph intersects
the y-axis are called the y -intercepts of the graph and are
obtained by setting x = 0 in the equation of the graph.

12. 12
Intercepts

13. 13
Example 8 –Finding Intercepts
Find the x-and y-intercepts of the graph of the equation
y = x
2
–2.
Solution:
To find the x-intercepts, we set y = 0 and solve for x. Thus
0 = x
2
–2
x
2
= 2
The x-intercepts are
Set y= 0
Add 2 to each side
Take the square root

14. 14
Example 8 –Solution
To find the y-intercepts, we set x = 0 and solve for y. Thus
y= 0
2
–2
y= –2
The y-intercept is – 2. Set x= 0
cont’d

15. 15
Example 8 –Solution
The graph of this equation is sketched in Figure 12 with the
x-and y-intercepts labeled.
Figure 12
cont’d

16. 16
Circles

17. 17
Circles

18. 18
Example 10 –Finding an Equation of a Circle
(a)Find an equation of the circle with radius 3 and center
(2, –5).
(b) Find an equation of the circle that has the points
P(1, 8) and Q(5, –6) as the endpoints of a diameter.
Solution:
(a)

19. 19
Example 10 –Solution
The graph is shown in Figure 16.
Figure 16
cont’d

20. 20
Example 10 –Solution
(b)
cont’d

21. 21
Example 10 –Solution
The graph is shown in Figure 17.
Figure 17
cont’d

22. 22
Symmetry

23. 23
Symmetry

24. 24
Example 12 –Using Symmetry to Sketch a Graph
Test the equation x = y
2
for symmetry

25. 25