ACTIVITY: Forming the Entire Coordinate Plane

Transcription

1 .5 The Coordinate Plane How can ou graph and locate points that contain negative numbers in a coordinate plane? You have alread graphed points and polgons in one part of the coordinate plane. In Activit, ou will form the entire coordinate plane. ACTIVITY: Forming the Entire Coordinate Plane Work with a partner. a. In the middle of a sheet of grid paper, construct a horizontal number line as shown. Label the tick marks. n a different sheet of grid paper, construct and label a similar vertical number line. 0 b. Cut out the vertical number line and tape it on top of the horizontal number line so that the zeros overlap. Make sure the number lines are perpendicular to one another. How man regions did ou form b doing this? c. REASNING What ordered pair represents the point where the number lines intersect? Wh do ou think this point is called the origin? Eplain. ACTIVITY: Describing Points in the Coordinate Plane CMMN CRE Coordinate Plane In this lesson, ou will describe the locations of points in the coordinate plane. plot points in the coordinate plane given ordered pairs. fi n dd is t a n c e s between points in the coordinate plane. Learning Standards MACC..NS..b MACC..NS..c MACC..NS..8 Work with a partner. Use our perpendicular number lines from Activit. a. Plot and label (, ) on our coordinate plane. Shade this region in our coordinate plane. What do ou notice about the integers along the number lines that surround (, )? b. Can ou plot a point in our coordinate plane so that it is surrounded b negative numbers on the aes? If so, where is this point? Use a different color to shade this region in our coordinate plane. c. What do ou notice about the integers along the number lines for points in the regions that are not shaded? d. STRUCTURE Describe how ou would plot (, ). How is plotting this point similar to plotting (, )? Plot (, ) in our coordinate plane. e. REASNING Where in our coordinate plane do ou plot (, )? Where do ou plot (, )? Eplain our reasoning. 7 Chapter Integers and the Coordinate Plane

2 Math Practice Check Progress How can ou check our progress to make sure ou are accuratel drawing the picture? ACTIVITY: Plotting Points in a Coordinate Plane Work with a partner. Plot and connect the points to make a picture. Describe and color the picture when ou are done. (, 9) (, ) (, ) (0, ) 5(, 9) (, ) 7( 9, ) 8(, ) 9( 7, 0) 0( 5, ) ( 5, 5) (, 8) (, 0) (, 9) 5(, 0) (, ) 7(, ) 8(, ) 9(, ) 0(, ) (, ) (, ) (, 0) (, 9) 5(, 9) (, 8) 7(, 0) 8(, ) 9(, ) 0(, ) (, ) (, ) (, ) (, ) 5(, 0) (, 8) 7(, ) 8(, 0) 9(9, ) 0(9, ) (8, ) (5, ) (, ) (, 7) 5(, 8) IN YUR WN WRDS How can ou graph and locate points that contain negative numbers in a coordinate plane? 5. Make up our own dot-to-dot picture. Use at least 0 points. Your picture should have at least two points in each region of the coordinate plane. Use what ou learned about the coordinate plane to complete Eercise on page 79. Section.5 The Coordinate Plane 75

3 .5 Lesson Lesson Tutorials Ke Vocabular coordinate plane, p. 7 origin, p. 7 quadrants, p. 7 Previousl, ou plotted points with positive coordinates. Now ou will plot points with positive and negative coordinates. The Coordinate Plane A coordinate plane is formed b the intersection of a horizontal number line and a vertical number line. The number lines intersect at the origin and separate the coordinate plane into four regions called quadrants. Quadrant II 5 Quadrant I -ais -ais 5 Quadrant III 5 5 Quadrant IV The origin is at (0, 0). An ordered pair is used to locate a point in a coordinate plane. ordered pair: (, ) -coordinate -coordinate EXAMPLE Identifing an rdered Pair Which ordered pair corresponds to point T? A (, ) B (, ) C (, ) D (, ) P S Point T is units to the right of the origin and units down. So, the -coordinate is and the -coordinate is. Q The ordered pair (, ) corresponds to point T. The correct answer is C. R T Eercises 5 Use the graph in Eample to write an ordered pair corresponding to the point.. Point P. Point Q. Point R. Point S 7 Chapter Integers and the Coordinate Plane

4 EXAMPLE Plotting rdered Pairs (, ).5 (0,.5) Plot (a) (, ) and (b) (0,.5) in a coordinate plane. Describe the location of each point. a. Start at the origin. Move units left and units up. Then plot the point. The point is in Quadrant II. b. Start at the origin. Move.5 units down. Then plot the point. The point is on the -ais. Eercises 5 EXAMPLE Plot the ordered pair in a coordinate plane. Describe the location of the point. 5. (, ). ( 5, 0) 7. (.5, ) 8. (, Finding Distances in the Coordinate Plane ) (, 5) (, ) 5 5 (, 5) (, ) An archaeologist divides an area using a coordinate plane in which each unit represents meter. The corners of a secret chamber are shown in the graph. What are the dimensions of the secret chamber? The length of the chamber is the distance between (, 5) and (, 5). The width of the chamber is the distance between (, 5) and (, ). You can use absolute values to find the distances between the points. Add the absolute values. Reading An archaeologist studies ancient ruins and objects to learn about people and cultures. 5 5 Subtract the absolute values. 5 5 The secret chamber is meters long and meters wide. Eercises In Eample, the archaeologist finds a gold coin at (, ), a silver coin at (, ), and potter at (, ). How much closer is the potter to the silver coin than to the gold coin? Section.5 The Coordinate Plane 77

5 You can use line graphs to displa data that is collected over a period of time. Graphing and connecting the ordered pairs can show patterns or trends in the data. This tpe of line graph is also called a time series graph. EXAMPLE Real-Life Application A blizzard hits a town at midnight. The table shows the hourl temperatures from midnight to 8:00 A.M. Hours after Midnight, Temperature, 7 F 5 F F 0 F F F 5 F F F Stud Tip The observations given in Eample (b) are sample answers. You can make man other correct observations. a. Displa the data in a line graph. Write the ordered pairs. (0, 7) (, 5) (, ) (, 0) (, ) (5, ) (, 5) (7, ) (8, ) Plot and label the ordered pairs. Then connect the ordered pairs with line segments. b. Make three observations from the graph. Three possible observations follow: Hourl Temperatures The hourl temperatures decrease from midnight to :00 a.m. The hourl temperatures increase from :00 a.m. to 8:00 a.m. The greatest decrease in hourl temperatures from one hour to the net is F. This happens twice: from :00 a.m. to :00 a.m. and from :00 a.m. to 5:00 a.m. Temperature (degrees Fahrenheit) (0, 7) (, 5) (, ) (, 0) (, ) (5, ) Hours after midnight (8, ) (7, ) (, 5) 0. In Eample, the blizzard hits another town at noon. The table shows the hourl temperatures from noon to :00 p.m. Hours after Noon 0 5 Temperature F 7 F 5 F F F 0 F F a. Displa the data in a line graph. b. Make three observations from the graph. 78 Chapter Integers and the Coordinate Plane

6 .5 Eercises Help with Homework. VCABULARY How man quadrants are in a coordinate plane?. VCABULARY Is the point (0, 7) on the -ais or the -ais?. WHICH NE DESN T BELNG? Which point does not belong with the other three? Eplain our reasoning. (, ) (, 5) (, ) (, ) 9+(-)= +(-)= +(-9)= 9+(-)=. Plot and connect the points to make a picture. (5, 0) (, ) (, ) (0, ) 5(, ) (, 0) 7(, ) 8(0, ) 9(, ) 0(, ) Write an ordered pair corresponding to the point. 5. Point A. Point B 7. Point C 8. Point D 9. Point E 0. Point F. Point G. Point H. Point I. Point J C G B H D A I E F J Plot the ordered pair in a coordinate plane. Describe the location of the point. 5. K(, ). L(, ) 7. M(0, ) 8. N(.5,.5) 9. P(, ) 0. R(, ). S ( ), 0. T(, 5) ERRR ANALYSIS Describe and correct the error in the solution... To plot (, 5), start at (0, 0) To plot (, ), start at (0, 0) and move 5 units right and and move units right and units up. units down. Plot the points and find the distance between the points. 5. (, ), (, ). (, ), (, ) 7. (, ), (, 7) 8. ( 5, ), (, ) 9. (, ), (5, ) 0. (, ), (, ) Section.5 The Coordinate Plane 79

7 . REASNING The coordinates of three vertices of a square are shown in the figure. What are the coordinates of the fourth verte? (, ) Draw the figure with the given vertices in a coordinate plane. Find the perimeter and the area of the figure.. D(, ), E(, ), F(, ), G(, ). P(, ), Q(5, ), R(5, ), S(, ). W(, ), X(, ), Y(, 7), Z(, 7) 5. PPULATIN The line graph shows the population of a cit from 005 to 0. a. Estimate the population of the cit in 0. b. Between which two ears did the population increase the most? c. Estimate the total change in population from 005 to 0. (, ). MDELING The table shows the total miles run through 8 weeks for a marathon training program. (, ) Week Total Miles Week Total Miles a. Create a table for the distance run during each week of training. b. Displa the data from part (a) in a line graph. c. Make three observations from the graph. d. Eplain the pattern shown in the graph. 7. PRFITS The table shows the profits of a compan from 007 to 0. Years since 000, Profit (millions of dollars), a. Displa the data in a line graph. b. Make three observations from the graph. c. What was the total profit from 007 to 0? d. How could ou include profits from the ears 990 to 00 on our graph? Eplain. Describe the possible location(s) of the point (, ). Population (thousands) 8. > 0, > 0 9. < 0, < 0 0. > 0, < 0. > 0. < 0. = 0, = Cit Population Year 80 Chapter Integers and the Coordinate Plane

8 Tell whether the statement is sometimes, alwas, or never true. Eplain our reasoning.. The -coordinate of a point on the -ais is zero. 5. The -coordinates of points in Quadrant III are positive.. The -coordinate of a point in Quadrant II has the same sign as the -coordinate of a point in Quadrant IV. Z In Eercises 7 5, use the map of the zoo. 7. Which ehibit is located at (, )? 8. Name an attraction on the positive -ais. 9. Is parking available in Quadrant II? If not, name a quadrant in which ou can park. 50. Write two different ordered pairs that represent the location of the Rain Forest. 5. Which ehibit is closest to ( 8, )? 8 Safari Africa 5 Parking The utback Flamingo Café 5 Tickets Reptiles 7 Parking Rain Forest Wetland Kaaking Eagles 5. NUMBER SENSE Name the ordered pair that is 5 units right and units down from (, ). 5. PEN-ENDED The vertices of triangle ABC are A(, ) and B(, ). List four possible coordinates of the third verte so that the triangle has an area of square units. 5. Your school is located at (, ), which is blocks east and block south of the center of town. To get from our house to the school, ou walk 5 blocks west and blocks north. a. What ordered pair corresponds to the location of our house? b. Is our house or our school closer to the center of town? Eplain. c. You can onl walk along streets that are north and south or streets that are east and west. You are at the center of town and decide to take the shortest path home that passes b the school. When ou are at the school, what percent of the walk home remains? Write the phrase as an epression. (Section.) 55. less than a number 5. the product of 8 and a number b 57. a number increased b a number w divided b 59. MULTIPLE CHICE What is the ratio of ducks to swans? (Section 5.) A : 9 B : 5 C 5 : D 5 : 9 Section.5 The Coordinate Plane 8