Plotting Ordered Pairs Using Integers

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3 Plotting Ordered Pirs Using Integers Ple two elsti nds on geoord to form oordinte xes shown on the right to help you solve these prolems.. Wht letter of the lphet does eh set of pirs nme?. (, ) (-, ) (-, ) (-, ) (, ) (, -) (, -) (-, -). (, ) (-, ) (, ) (, -). These ordered pirs nme points tht form the outline of fmilir ojet (-, -) (, ) (, -) (-, ) (, ). Wht is it?. These sets of ordered pirs nme points tht form the outlines of fmilir geometri shpes. Nme them.. (, ) (, ) (, -) (, -) (-, -) (-, ) (, ). (, -) (, -) (-, ) (-, ) (, -). Plot nd onnet these points in order using elsti nds: (, ) (-, -) (, ) (-, ) (, -) (, ). Wht is it? 5. Write set of ordered pirs tht n e used to uild the numerl elow Mke set of ordered pirs to form these letters of the lphet: Z I P. 7. Crete the outline of fmilir ojet using elsti nds on your grid (tree, silot, et.). Reord the nme of the ojet you uild nd the set of ordered pirs required to rete it in the spe elow.

4 Exploring Midpoints of Line Segments We know it is esy to onstrut line segment on geoord or dot pper nd then put our finger on the midpoint of the segment. In this lesson we will explore more preise method of finding midpoints of segments y using oordintes. Set up xes on geoord like the exmple to the right. Then omplete the exerises tht follow.. Here re three line segments. Wht re the oordintes of the endpoints of eh segment? B C D A A A. Mrilyn mde tle to show the oordintes of eh endpoint nd the oordintes of eh midpoint. Complete the tle elow. Segment Endpoint Coordintes Midpoint Coordintes AB AC AD. Mrk sid he ould write the oordintes of the midpoint for ny point on geoord if one of the endpoints is (, ) y using this tle. Is he orret? Explin. Endpoint Coordintes Midpoint Coordintes (, ) (, d) ( d, d)

5 Exploring Midpoints of Line Segments. Mi wondered if she ould find the oordintes of the midpoint of ny horizontl or vertil line segment on geoord y modifying the tle in Exerise. Help her finish the tle. Segment Type Endpoint Coordintes Midpoint Coordintes Horizontl Vertil (, ) (, ) (r, s) (r, t) 5. Use the tle you ompleted in Exerise to help find the midpoint of eh segment. The oordintes of the endpoints for eh segment re provided.. (, ) (, ). (, ) (, ) 6. Set up this segment on geoord.. Wht re the oordintes of the endpoints of the segment EZ?. Wht re the oordintes of the midpoint of the segment EZ? E Z 7. Josh sid the oordintes for the midpoint of ny segment on geoord n e found using the tle elow. Is he orret? Give exmples to support your nswer. Endpoint Coordintes (, ) (, d) Midpoint Coordintes ( ( + ), ( + d) ) 5

6 Exploring Tringles Supposed you hd miniture geoord like this:. How mny tringles n e uilt on the miniture geoord tht re ongruent to the exmple?. How mny different right ngles n e uilt?. How mny different tringles n e uilt? Reord your nswers for eh prolem elow or on dot pper. 6

7 True or Flse. Look t eh figure in the first olumn. Then, fill in the row y writing T if the heding is true nd F if it is flse. Polygon Squre Retngle Prllelogrm Trpezoid Qudrilterl... d. e. 7

8 True or Flse. Fill in the missing polygons nd other entries. Polygon Squre Retngle Prllelogrm Trpezoid Qudrilterl. True True True. True. Flse Flse True d. Flse e. Flse Flse True 8

9 The Pythgoren Theorem Construt the tringles shown on the next pge on your geoord or dot pper. One this hs een done, use your metri ruler nd your lultor to omplete the hrt elow. Mesure eh side to the nerest millimeter. The first prolem hs een ompleted for you. ² ² ² + ² ² Wht ptterns do you notie? 9

10 The Pythgoren Theorem Bonus: Wht is the digonl length of this TV monitor?? 56

11 Seleted Answers nd Comments: Plotting Ordered Pirs Using Integers... S. T. Arrow.. Hexgon. Retngle. A Str 5. Ordered pirs strting from the top nd moving to the ottom: (, ) (, ) (-, ) (-, ) (, ) (, -) (, -) (-, -) 6. Z = (-, ) (, ) (-, -) (, -) I = (-, ) (, ) (, ) (, -) (-, -) (, -) P = (-, -) (-, ) (, ) (, ) (-, ) 7. Answers my vry. Exploring Midpoints of Line Segments.. Segment AB AC AD Endpoint Coordintes (, ) & (, ) (, ) & (, ) (, ) & (, ) Midpoint Coordintes (, ) (.5,.5) (,.5). No. It should e (( + ) /, ( + d) / ) or (() /, (d) / ). Horizontl (( + ) /, ). Vertil (r, (s + t) / ). 6. (, ) nd (, ). The midpoint oordintes re (.5,.5). 7. No. The orret oordintes for the midpoint re (( + ) /, ( + d) / ). Qudrilterl True or Flse... TTTFT. FTTFT. FFTFT d. FFFTT e. FTFTT. Answers my vry.. Flse, True. Flse, Flse, Flse, True. Flse, True d. Flse, Flse, Flse, Flse e. Flse, Flse The Pythgoren Theorem. Pttern nswers my vry. Most students note tht ll the tringles re right tringles nd tht + =. Bonus: 7. Some lsses enjoy finding the missing dimensions of other TV sets. For exmple, wht is the height of TV set if the width is 8 nd the digonl is 5? =?, = 8, = 5. Exploring Tringles. Some students will dete the mening of the word different in this explortion. In this tivity, different mens not ongruent. So, if tringle is uilt in different lotion ut is the sme size nd shpe, it is not ounted. Other students will question if the verties must e on the nils. The nswer is yes. These re gret questions. Enjoy the fun Hint: More thn 7.