The document provides examples and explanations for using the coordinate plane: - It defines the key elements of the coordinate plane including the x-axis, y-axis, origin, quadrants, and ordered pairs used to identify points. - An example shows how to plot the point (4, -2) by moving right 4 units and down 2 units from the origin. - Another example solves a multi-step problem to find the perimeter of a rectangular region on a coordinate plane by identifying the coordinates of its vertices and calculating the length and width.

1. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to simplify or write an equivalent expression. – 8( f + 2 + 3) 2. 1. 2( w – 8)

2. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to simplify or write an equivalent expression. = 2 w – (2)(8) = 2 w – 16 – 8( f + 2 + 3) 2. = -8f + (-8)(2) + (-8)(3) = -8f + -16 + -24 = -8f + -40 1. 2( w – 8)

3. 2.8 Coordinate Plane

4. The Coordinate Plane -5 -5 5 5

5. Imagine the top surface of your desk stretching in every direction. If it continued to spread , it would go right through your neighbor . . .

6. . . . and then through the classroom walls . . .

7. Then you would have a plane .

8. In mathematics, a plane is a flat surface that goes on forever in every direction. We often use the coordinate plane .

9. The coordinate plane is divided by two number lines. One is horizontal, like the number line you already know.

10. -5 5 0 10 -10

11. The other is vertical, with up being the positive direction and down being the negative direction.

12. -5 5 0 10 -10 5 -5

13. The coordinate plane is filled with points . . .

14. . . . infinitely many points. And somewhere among all those points is the point we call the origin .

15. The origin is the point where the two number lines meet. -5 5 0 10 -10 5 -5

16. The two number lines have special names. The horizontal number line is called the x -axis. -5 5 0 10 -10 5 -5

17. The vertical number line is called the y -axis. -5 5 0 10 -10 5 -5

18. To study a point, we need to know where to find it. So we give it coordinates. Coordinates are like an address. They tell you how you can get to a point if you start at the origin.

19. Coordinates are always written in parentheses, with the x -value first. -5 5 0 10 -10 5 -5

20. Coordinates written in parentheses are called an ordered pair . -5 5 0 10 -10 5 -5

21. Consider the point which has coordinates, (4, -2) -5 5 0 10 -10 5 -5

22. The first number tells you how far to move to the side. -5 5 0 10 -10 5 -5

23. So the 4 in (4, -2) says we need to move 4 units to the right. Remember to start at the origin. -5 5 0 10 -10 5 -5

24. The second number tells you how far to move up or down. -5 5 0 10 -10 5 -5

25. The –2 in (4, -2) tells you to move down two units. -5 5 0 10 -10 5 -5

26. To get to the origin from the origin, we don’t move at all. So the origin is designated by the ordered pair, (0, 0) -5 5 0 10 -10 5 -5

27. The two number lines divide the plane into four regions. Quadrants are labeled with Roman Numerals. We call the regions quadrants. -5 5 0 10 -10 5 -5

28. In Quadrant I, all numbers are positive. In Quadrant II, x -values are negative, while y -values are positive. In Quadrant III, x - and y -values are both negative. In Quadrant IV, x -values are positive and y -values are negative. -5 5 0 10 -10 5 -5

30. Give the coordinates of each point:

31. Give the coordinates of each point:

32. Tell how you can find each point: Remember to start at the origin! From the origin, move to the right 8 units, then down 7 units.

33. Graph the points and tell which quadrant they are in :

34. EXAMPLE 3 Solve a Multi-Step Problem Archaeology On a field trip, students are exploring an archaeological site. They rope off a region to explore as shown. Identify the shape of the region and find its perimeter . The units on the scale are feet.

35. EXAMPLE 3 Solve a Multi-Step Problem SOLUTION STEP 1 Notice that points A, B, C, and D form a rectangle. Find the coordinates of the vertices. STEP 2 Find the horizontal distance from A to B to find the length l . A (–30, 20) , B (30, 20) , C (30, –20) , D (–30, –20) x - coordinate of B x - coordinate of A = l – = – 30 – 30 – 60 = = 60

36. EXAMPLE 3 Solve a Multi-Step Problem STEP 3 Find the vertical distance from A to D to find the width w . STEP 4 Find the perimeter: 2 l + 2 w = 200 . y - coordinate of D y - coordinate of A = w – = 20 – ( –20 ) 40 = = 40 = 2(60) + 2(40) ANSWER The region’s perimeter is 200 units 10 feet per unit = 2000 feet .