1. LESSON How do you locate and name points in the coordinate plane? Graphing on the Coordinate Plane 14.1

2. Warm Up Graph each integer and its opposite on a number line. 1. 4 2. –7 3. –2 Graph the integers on a number line. 4. 7, –2, 0, 3, –5 1 2 3 4 5 6 7 8 –8–7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –8–7–6 –5–4 –3 –2 –1 0

3. x y –2 2 2 –4 4 4 –1 –3 –5 A coordinate plane is a plane containing a horizontal number line, the x-axis, and a vertical number line, the y-axis. The intersection of these axes is called the origin. The axes divide the coordinate-plane into four regions called quadrants, which are numbered I, II, III, and IV. 5 3 1 1 3 5 0 –3 –5 –1 Quadrant I Quadrant IV Quadrant II Quadrant III Origin x-axis y-axis

4. Identify the quadrant that contains each point. Additional Example 1: Identifying Quadrants on a Coordinate Plane A. S S lies in quadrant IV. B. T T lies in quadrant I. C. W W lies on the y-axis between Quadrants I and II W S T x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

5. Check It Out: Example 1 Identify the quadrant that contains each point. A. N N lies in quadrant II. B. X X lies in quadrant III. C. Y Y lies on the origin. N X Y x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

6. Points on a coordinate plane are identified by ordered pairs. An ordered pair consists of two numbers in a certain order. The origin is the point (0,0). Ordered pair (3, 2) x-coordinatey-coordinate Units right or left from 0 Units up or down from 0 x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1 3 units right 2 units up

7. Plot each point on a coordinate plane. Additional Example 2: Plotting Points on a Coordinate Plane A. D (3, 3) Start at the origin. Move 3 units right and 3 units up. B. E (–2, –3) Start at the origin. Move 2 units left and 3 units down. C. F (3, –5) Start at the origin. Move 3 units right and 5 units down. F D E x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

8. Check It Out: Example 2 Plot each point on a coordinate plane. A. D (4, 4) Start at the origin. Move 4 units right and 4 units up. B. E (–2, 3) Start at the origin. Move 2 units left and 3 units up. C. F (–1, –2) Start at the origin. Move 1 unit left and 2 units down. F D E x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

9. Give the coordinates of each point. Additional Example 3: Identifying Points on a Coordinate Plane A. X Start at the origin. Point X is 2 units left and 5 units up. B. Y Start at the origin. Point Y is one unit left on the x-axis. C. Z Start at the origin. Point Z is 3 units right and 3 units down. (–2, 5) (–1, 0) (3, –3) Z X Y x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

10. Check It Out: Example 3 Give the coordinates of each point. A. L Start at the origin. Point L is 4 units left and 3 units up. B. M Start at the origin. Point M is 2 units left and 2 units down. C. N Start at the origin. Point N is 3 units right and 4 units up. (–4, 3) (–2, –2) (3, 4) N L M x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1

11. ADDITIONAL EXAMPLE 1 Identify the coordinates of each point. Name the quadrant where each point is located. Point A: (3, –2), Quadrant IV; Point B: (–4, 1), Quadrant II

12. ADDITIONAL EXAMPLE 2 Graph and label each point on the coordinate plane. P(0, –2), Q(–4, 1.5), R(3.5, 0)

13. ADDITIONAL EXAMPLE 3 The graph shows the location of a fountain, a slide, and a sandbox in a park. The scale on each axis represents yards. Give the coordinates for the sandbox and use them to describe the location of the sandbox relative to the fountain. The sandbox is at (10, –15). This is 10 yards east and 15 yards south of the fountain.

14. Lesson Quiz: Part I Give the coordinates of each point and identify the quadrant that contains each point 1. A(–2, 4); II 2. B(3, –2); IV 3. C (2, 3); I Plot each point on a coordinate plane. 4. D (2, –3) 5. E (–4, –2) B A C x y –2 2 2 –4 4 4 –1 –3 –5 5 3 1 1 3 5 0 –3 –5 –1 D E

15. Lesson Quiz: Part II 6. To plot (7, –2) a student started at (0, 0) and moved 7 units left and 2 units down. What did the student do wrong? He should have moved 7 units right.

16. Plot the points for each set of ordered pairs below. Then connect the points in the order shown to reveal a figure. Name the figure and find its area. Set 1: (2, 5), (2, –1), (– 3, –1), (–3, 5) Set 2: (–4, –3), (6, –3), (6, 4) Set 3: (1, 3), (–4, 3), (–4, –2), (1, –2) Set 1: rectangle, A = 30 square units Set 2: triangle, A = 35 square units Set 3: square, A = 25 square units

17. How do you locate and name points in the coordinate plane? Sample answer: Points in the coordinate plane are located and named by their locations from the origin along the x-axis first, followed by the y-axis. The order of the coordinates is important.