cuadernillo-geogebra

8/16/2019 cuadernillo-GEOGEBRA

1/46

!! #$%&'(')

)$*%+

,+$-+*%'

+& .&('/012'

.*%3/ 4566

!"#$%$&'&() +',' (- .'--(,/

!"#$%&'()#*"

,"#

" #$ %&'($ )$#*+,-

./ ( 0*-*1$1 %$'(*++& " $0$

./ , -)"+"' # $0(2- ($3*$'

!"#$%&'()#*" ,"# -)".)/&0

! ' 0 * ) & # 1

2 2 " * ) 0 , % 1 3 1 * 0 * ) $


2/46

2


3/46

1

!"#$%&

() *$+,-$. / 0$1&%,-$.

2) 3"45671

8) 3"45671 #& 976!47"71

:) 6!"&+1 / 95",71 "7,+06&1 #& 5" ,-$3"4567

;) ,&7-&*+1 -&6+%$7"+#71 %7" 671 ,-$3"45671


4/46

2


5/46

3

!"

#$%&"'(&)*

!" !"#$%&'$( #$ %& '$()$&*+ $' ," -$.*" /$-/$.%,"- ", '$()$&*+ $& '% /%&*+ )$#0+1

)*&$+$#%#", *-. /"-0"1'%2

2+&'*-%3$ ," )$#0"*-045 ) #$ %& '$()$&*+ 67 )"&%",)$&*$1 8+ %*0,0.$' $, 9+*:& )$#0"*-041 ;%$%? /-+/0$#"# .%)/,$& ,+' /%&*+' #$ )5 .+&

-$'/$.*+ " $,,+'@ A09%B" #+' '$()$&*+' 67 3 72 C>%$ '$ .+-*$& $& 7D1 2+&'*-%3$ '%' -$'/$.*0%? /%&*+ #$ %&" %$ '$ $&.%$&*-$ " ," )0')" #0'*"&.0" #$ ,+' /%$9,+' 6 3 7@

*$+,-$. / 0$1&%,-$.


6/46

4

!" +&,$-'(&)*

!" 8$,"*&'$(

#$

%&

J&(%,+

$'

%&"

'$)0--$.*"

>%$

#0%0#0'*"& #$ ,+' ,"#+' #$, J&(%,+1

)*&$+$#%#", *-. /"-0"1'%2

E$",04" ," .+&'*-%..0:& "&*$-0+-K 2+&'*-%3$ ," 90'$.*-045 9 #$ #+' '$)0--$.*"' - 3 '1 C)"&%",)$&*$5 &+ %*0,0.$' $, 9+*:& 90'$.*-04D1 L$M"," %& /%&*+ A $& 91 N-"4" ,"' /$-/$.%,"-$' AF 3 AO -$'/$.*+ #$ - 3 '1 2+)/-%$9" >%$ DE = DF =P"3 /%&*+' #$ ," 90'$.*-04 >%$ &+ $'*?& " ," )0')" #0'*"&.0" #$ ,+' ,"#+'@ =Q+- >%?@

F& %& J&(%,+ .%",>%0$-"5 .+&'*-%3$ %&" .0-.%&H$-$&.0" #$ R .)1 #$ -"#0+ >%$ '$" *"&($&*$ " ,+' #+' ,"#+' #$, J&(%,+ C'+,+ *+>%$ $& %& /%&*+ " ."#" ,"#+ #$, J&(%,+D1

)*&$+$#%#", 3%'% "4 %54%2

67 F& $, J&(%,+ ˆ º80 42 56 A 5 *-"4")+' '% 90'$.*-045 =.%J&*+ )0#$ ."#" J&(%,+

-$'%,*"&*$@


7/46

5

./",&0&-"-&12

%$

/3,

4256/3,*

S& J&(%,+ $' '"*&-5 .%"+ )0#$ TUV

S& J&(%,+ $' 44%.-5 .%"+ )0#$ WXUV

S& J&(%,+ $' %05#- .%"+ $' )$&+- >%$ %&+ -$.*+5 .%"+ $' )"3+- '$ ,,")" -1&5,- 1

S& J&(%,+ $' *-.+"9- .%"+ $' )$&+- >%$ %&+ ,,"&+5 .%"+ $' )"3+- '$ ,,")" *:.*%+- 1

)*&$+$#%#", *-. /"-0"1'%2

;%$


8/46

6

7$/"-&32$, 4256/"($,*

A+' J&(%,+' '+& *-;34";".&%'$-, .%"+ '% '%)" $' %&+ -$.*+5 TUV1 L+& ,534";".&%'$-, .%"+ '% '%)" $' %&+ ,,"&+5 WXUV

A+' J&(%,+' '+& *-.,"*5&$+-, .%"+ *0$&$& $, )0')+


9/46

7

8256/3, 96$ ,$ 03(:"2 "/ -3('"( %3, ($-'", ;"("/$/", ;3( 62" ,$-"2'$*

L0 #+' -$.*"' /"-",$,"' '$ .+-*"& /+- %&" -$.*" '$."&*$ " ?'*"'5 '$ H+-)"& +.I+ J&(%,+'5 )%.I+' #$ ,+' .%",$' 0(%",$' $&*-$ 'G1

)*&$+$#%#", *-. /"-0"1'%2

L0 )%$


10/46

8


11/46

9

@-'-4%'$-,2

F& *+#+ *-0J&(%,+5 ."#" J&(%,+ $' 0(%", " WXU_ )$&+' ," '%)" #$ ,+' +*-+'

#+' J&(%,+'1

L0 $& %& *-0J&(%,+ %& J&(%,+ $' -$.*J&(%,+ % +9*%'+5 ,+' #+' J&(%,+' -$'*"&*$' '+& "(%#+'1

L0 #+' *-0J&(%,+' *0$&$& #+' J&(%,+' 0(%",$'5 ,+' *$-.$-+' *")90?& '+& 0(%",$'1

)*&$+$#%# *-. 0"-0"1'%2

2+&'*-%3$ %& *-0J&(%,+ -$.*J&(%,+ 3 .+)/-%$9" >%$ ," '%)" #$ '%' J&(%,+' $' WXUV

)*&$+$#%#", 3%'% "4 %54%2

67 L0 .+&+.$)+' #+' J&(%,+' #$ %& *-0J&(%,+ ˆ ˆ36º y B=48º A 5 =.%J&*+

/+#$)+' #$.0- >%$ )0#$ $, J&(%,+ Ĉ @

>7 L0 $& %& *-0J&(%,+ 0':'.$,$' ,+' J&(%,+' 0(%",$' )0#$& Y`V5 =.%J&*+ )$#0-J $, J&(%,+ #$'0(%",@

A7 A$*$-)0&" $,


12/46

10


13/46

11

)*&$+$#%# *-. /"-0"1'%2

2+&'*-%3$ %& *-0J&(%,+ 6725 -$.*J&(%,+ $& 6 3 .+)/-%$9" >%$ $, J&(%,+

$a*$-0+- $&

7

.+0&.0#$

.+&

,"

'%)"

#$

,+'

0&*$-0+-$'

&+

"#3".$&*$'1

)*&$+$#%#", 3%'% "4 %54%2

67 2",.%," ," )$#0#" #$ *+#+' ,+' J&(%,+' #$, '0(%0$&*$ *-0J&(%,+ 0':'.$,$'K

>7 F& %& *-0J&(%,+ 0':'.$,$'5 $, J&(%,+ $a*$-0+- #$,


14/46

12

8256/3, &2'$(23, $2 62 ;3/>5323*

!" '%)" #$ ,+' J&(%,+' #$ .%",>%0$- *5%#'$4B&"'- $' Y`UV

)*&$+$#%#", *-. /"-0"1'%2

=F' /+'09,$ .+&'*-%0- %& .%"#-0,J*$-+ .+& %& ]&0.+ J&(%,+ -$.*+@ =b .+& #+'@ =b .+& *-$'@

A$)%$'*-" >%$ ," '%)" #$ ,+' J&(%,+' 0&*$-&+' #$ %& *-0J&(%,+ $' WXUV1 =2%J, $' $,


15/46

13

8256/3, $='$(23, %$ 62 ;3/>5323*

S& B.054- "9&"'$-' + B.054- "9&"'.- $' $, J&(%,+ H+-)"#+ /+- %& ,"#+ #$ %& /+,G(+&+ 3 ," /-+,+&(".0:& #$, ,"#+ "#3".$&*$1

)*&$+$#%#", *-. /"-0"1'%2

E$",04" ," )0')" #$)+'*-".0:& /"-" %& I$aJ(+&+1

E"4+&" >%$ +.%--$ $&*-$ ,+' J&(%,+' $a*$-0+-$' $ 0&*$-0+-$' #$ %& /+,G(+&+5 =>%? -$,".0:& "&(%,"- ,+' %&$@

F& ($&$-",5 =.%J&*+ )0#$ ," '%)" #$ ,+' J&(%,+' $a*$-0+-$' #$ .%",>%0$- /+,G(+&+@

)*&$+$#%#", 3%'% "4 %54%2

67 2",.%," ," )$#0#" #$ ,+' J&(%,+' #$'.+&+.0#+'K


16/46

14

!" ;"#$%&'$( #$ %& ,"#+ #$, *-0J&(%,+ $' ," -$.*" /$-/$.%,"- " ?,5 >%$ /"'" /+- $, /%&*+ )$#0+1

)*&$+$#%#", *-. /"-0"1'%2

!"' *-$' )$#0"*-0.$' #$ ,+' ,"#+' #$ %& *-0J&(%,+ '$ .+-*"& $& %& /%&*+5 *$'*5.*".&'- 5 >%$ $>%0#0'*" #$ ,+' *-$'


17/46

15

)*&$+$#%# *-. /"-0"1'%2

!"' *-$' 90'$.*-0.$' #$ %& *-0J&(%,+ '$ .+-*"& $& %& /%&*+5 0&.$&*-+5 >%$ $>%0#0'*" #$

,+' *-$'

,"#+'

#$,

*-0J&(%,+

3 >%$

$'

$,

.$&*-+

#$

,"

.0-.%&H$-$&.0"

0&'.-0*"1

2+&'*-%3$

,"

.0-.%&H$-$&.0" 0&'.-0*" " %& *-0J&(%,+1

)*&$+$#%#", 3%'% "4 %54%2

W1 2+&'*-%3$ ," .0-.%&H$-$&.0" .0-.%&'.-0*" ", *-0J&(%,+ #$


18/46

16

?$3($:"

%$


19/46

17

)*&$+$#%#", 3%'% "4 %54%2

W1 A09%B" .+& c$+($9-" %& *-0J&(%,+ -$.*J&(%,+ 3 .+)/,$*" $, '0(%0$&*$ *$a*+K

!+' ,"#+' #$, *-0J&(%,+ )0#$& -$'/$.*0


20/46

18

@'(3, '$3($:", %$/ '(&4256/3*

?"-'";%

#"

4%

%4&5'%2 F,

/-+#%.*+

#$

,+'

#+'

."*$*+'5

#$

%&

*-0J&(%,+

-$.*J&(%,+5

.+0&.0#$ .+& $, /-+#%.*+ #$ ," I0/+*$&%'" /+- ," ",*%-" '+9-$ $,,"

@-. /"-0"1'%2

)*&$+$#%# *-. /"-0"1'%2

P"4 %&" .+&'*-%..0:& .+& c$+($9-" /"-" /-+9"- $, N$+-$)" #$, 2"*$*+K

?"-'";% #"4 @%&"&-2 F, .%"#-"#+ #$ %& ."*$*+ $' 0(%", ", /-+#%.*+ #$ ," I0/+*$&%'" /+- ," /-+3$..0:& #$, ."*$*+ '+9-$ ," I0/+*$&%'"1


21/46

19

)*&$+$#%#", 3%'% "4 %54%2

W1 2",.%," $, J-$" '+)9-$"#" $& ," H0(%-" '0(%0$&*$K

[1 =6 >%? #0'*"&.0" #$ 6 $'*J '0*%"#+ $, /%&*+ ; '0 '$ '"9$ >%$ ," #0'*"&.0" $&*-$ F 3 2 $' #$ X .)15 $&*-$ 2 3 6 $' #$ Z .)1 3 $&*-$ A 3 2 $' #$ [ .)1@

?"-'";% #" ?%4",2 S&" '$-0$ #$ -$.*"' /"-",$,"' >%$ .+-*"& " #+' -$.*"' .+&.%--$&*$' #$*$-)0&"& $& %&" #$ $,,"' '$()$&*+' /-+/+-.0+&",$' " ,+' .+--$'/+$&*$' #$*$-)0&"#+' $& ," +*-"1 b ", -$


22/46

20

2+& c$+($9-" /+#$)+' .",.%,"- J-$"' '0)/,$)$&*$ %*0,04"+ ," I$--")0$&*" J-$" + 90$& %*0,04"+ ," .%"#-G.%,"1 ^&.,%'+ /+#$)+' .",.%,"- J-$"' #$ 0)J($&$'1

Q$-+ &+'


23/46

21

A/ 4($" %$ 62 '(&4256/3 $, /" :&'"% %$ /" %$ 62 ;"("/$/35(":3*

)*&$+$#%#", *-. /"-0"1'%2

W1 2+)/-%$9" >%$ $, J-$" #$, *-"/$.0+ $' ," )0')" >%$ $, J-$" #$, /"-",$,+(-")+ #$ 9"'$ ," '%)" #$ ,"' 9"'$' #$, *-"/$.0+ 3 #$ ",*%-" ," )0*"#1

[1 2",.%," $, J-$" #$ ,"' /0'*"' #$, 0&'*0*%*+1

Y1

2",.%," $,

J-$"

#$

,"

'0(%0$&*$

H0(%-"


24/46

22

A/ 4($" %$ 62 ;3/>5323 ($56/"( ,$ ";(3=&:" "/ 4($" %$/ ->(-6/3 $2 $/ 96$ $,'4 &2,-(&'3C " :$%&%" 96$ -($-$ $/ 2D:$(3 %$ /"%3,*


25/46

23

.32,'(6--&12 %$ /" -&(-620$($2-&"*

?"-'";% 6K @$'*5.C"'".*$% F5" 3%,% 3-' #-, 35.&-,

F, ,%("- ($+)?*-0.+ #$, .$&*-+ #$ ,"' .0-.%&H$-$&.0"' >%$ /"'"& /+- #+' /%&*+' 6 3 7 $' ," )$#0"*-04 #$, '$()$&*+ 671

c$+)?*-0.")$&*$K

?"-'";% >K @$'*5.C"'".*$% F5" 3%,% 3-' &'", 35.&-,

Q+- *-$' /%&*+' #$, /,"&+ &+ ",0&$"#+' /"'" %&" 3 ':,+ %&" .0-.%&H$-$&.0"1

@-'-4%'$-2

A+' .0-.%&H$-$&.0"'

#0'*0&*"'

/%$#$&

.+-*"-'$5

" ,+

'%)+5

$&

#+'

/%&*+'1

)*&$+$#%#", *-. /"-0"1'%2

A$)%$'*-" $, *$+-$)" [1 =j%0?& $' $'" .0-.%&H$-$&.0"@

C^.".0:&K *-$' /%&*+' &+ ",0&$"#+' H+-)"& %& *-0J&(%,+D

6+ %$-%5"=&-&"%$+


26/46

24

%$ -$/-$'$&*" ," #0'*"&.0" )J' .+-*" #$'#$ $, .$&*-+ #$ ," .0-.%&H$-$&.0" " ," -$.*" , 5 =>%? J&(%,+ H+-)"& ,"' -$.*"' , 3 ' @ ;%$'*-" ," #0'*"&.0" #$, -"#0+ 3 #$, '$()$&*+ >%$ %&$ $, .$&*-+ #$ ," .0-.%&H$-$&.0" 3 ," 0&*$-'$..0:& #$ , 3 ' 1 ;%$


27/46


28/46

26

8256/3, $2 62" -&(-620$($2-&"*

l&(%,+ *".&'%4 $' $, >%$ *0$&$ '%


29/46

27

?"-'";%2 IJ.054- $.,*'$&- ". 5.% ,";$*$'*5.C"'".*$%H

N+#+ J&(%,+ .%3+


30/46

28

L$" %& '$()$&*+ 675 '$ #$&+)0&" %'*- *%3%( #$ 67 /"-" %& J&(%,+ ", ,%("- ($+)?*-0.+ #$ ,+' /%&*+' #$, /,"&+ ;5 *",$' >%$ ˆ AMB 1

@%,-, 3%'&$*54%'",7

F, "-.+ ."/"4 #$ %& J&(%,+ -$.*+5 .+&'*-%0#+ '+9-$ $, '$()$&*+ $' %&" '$)0.0-.%&H$-$&.0" #$ #0J)$*-+ 671

F, ,%("- ($+)?*-0.+ #$,


31/46

29

?'%,4%*$:.2

?'%,4%*$:. I,$. #",4$(%#-'",HKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

N-"',".0:& #$ %& +9B$*+K

?'%,4%*$:. #" 5.% $;%0".2

)*&$+$#%# *-. 0"-0"1'%2

2+&'*-%3$ %& /$&*J(+&+ -$(%,"- 3 *-"',J#",+ )$#0"&*$ $,


32/46

30

)*&$+$#%# *-. 0"-0"1'%2

2+&'*-%3$ %& /+,G(+&+ #$ ` ,"#+' 3 *-"',J#",+ )$#0"&*$ $,


33/46

31

G&:$'(>",*

G$;"&'L% *".&'%4KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

!" '0)$*-G" .$&*-",5 $& ($+)$*-G"5 $' %&" *-"&'H+-)".0:& $& ," >%$ " ."#" /%&*+ '$ ,$ "'+.0" +*-+ /%&*+5 >%$ #$9$ .%)/,0- ,"' '0(%0$&*$' .+.0+&$'K

"D F, /%&*+ 3 '% 0)"($& $'*J& " 0(%", #0'*"&.0" #$ %& /%&*+ ,,")"#+ .$&*-+ #$ '0)$*-G"1

9D F, /%&*+5 '% 0)"($& 3 $, .$&*-+ #$ '0)$*-G" /$-*$&$.$& " %&" )0')" -$.*"1

L0)$*-G" .$&*-", #$, /%&*+ 61 L0)$*-G" .$&*-", #$, *-0J&(%,+ 6725

-$'/$.*+ #$, /%&*+ d1

)*&$+$#%# *-. /"-0"1'%2

2+&'*-%3$ %& /+,G(+&+ 0--$(%,"- #$ Z ,"#+' 3 *-"4" '% '0)?*-0.+ -$'/$.*+ #$ %& /%&*+ .%",>%0$-"5 d1


34/46

32

G$;"&'L% %9$%4KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

!" '0)$*-G" "a0", $' $, )+%$ *-"&'H+-)" *+#+' ,+' /%&*+' #$ %& +9B$*+ $& +*-+ 0#?&*0.+5 *+)"+ .+)+ -$H$-$&.0" %& !"! #! $%&!'()*1 F' #$.0-5 $& %&" '0)$*-G" "a0", " ."#" /%&*+ #$ %&" H0(%-" '$ ,$ "'+.0" +*-+ /%&*+ ,,")"#+ 0)"($&5 >%$ .%)/,$ .+& ,"' '0(%0$&*$' .+.0+&$'K

"D !" #0'*"&.0" #$ %& /%&*+ 3 '% 0)"($& ", $B$ #$ '0)$*-G"5 $' ," )0')"1

9D F, '$()$&*+ >%$ %&$ %& /%&*+ .+& '% 0)"($&5 $' /$-/$.%,"- ", $B$ #$ '0)$*-G"1

L0)$*-G" "a0", #$, /%&*+ 61 L0)$*-G" "a0", #$ %& *-0J&(%,+1

F& %&" '0)$*-G" "a0", /$-)"&$.$& 0&%$ &+ $, '$&*0#+ #$ ,+' J&(%,+'1

)*&$+$#%# *-. /"-0"1'%2

A$'$")+' $)9",#+'"- %& '%$,+ .+& *-0J&(%,+' $>%0,J*$-+'1 S*0,04" ,"' '0)$*-G"' "a0",$' /"-" .+&'$(%0-,+1


35/46

33

@-;3-,$*$:. #" ,$;"&'L%,KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

L0 '$ "/,0." ," )0')" '0)$*-G" #+'


36/46

34

/$'-,2

/$'- ,$. #",4$(%#-'KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

S& (0-+ #$ .$&*-+ D 3 J&(%,+ $' %& )+%$ " ."#" /%&*+ #$, /,"&+ 75 ,$ I".$ .+--$'/+$- +*-+ /%&*+ #$, /,"&+ 7n5 #$ H+-)" >%$ ," #$,&%.*$% #$ D " 8 $' ," )0')" >%$ ," #0'*"&.0" #$ D " 8M 3 $, J&(%,+ H+-)"#+ /+- ,+' '$()$&*+' D8 3 D8M


37/46

35

)*&$+$#%# *-. /"-0"1'%2

2+&'*-%3$ %& /$&*J(+&+ -$(%,"- 3 I"4,+ (0-"- .+& %& #$',04"#+- '+9-$ '% .$&*-+

)*&$+$#%#", 3%'% "4 %54%2

W1 2+&'*-%3$ %& I$aJ(+&+ -$(%,"- 3 I"4,+ (0-"- '+9-$ '% .$&*-+ .+& %& J&(%,+ #$ (0-+ C$&*-$ U 3 Y`U (-"#+'D1 d9'$-%? J&(%,+' #$ (0-+5 ," H0(%-" (0-"#" .+0&.0#$ .+& ," #$ /"-*0#"@

9D L$ *-"*" #$ %&" H0(%-" .+& '0)$*-G" #$ (0-+5 =#$ >%? +-#$&@

.D 6#$)J' #$ '0)$*-G" #$ (0-+5 =*0$&$ ," H0(%-" 0&0.0", ",(]& $B$ #$ '0)$*-G"@

[1 F& )%.I+' #$ ,+' ,+(+*0/+' #$ ,"' )"-."' 3 $)/-$'"' /+#$)+' $&.+&*-"-&+'

.+& H+-)"' .-$"#"' "/,0."+ (0-+'1 =Q+#-G"' $&.+&*-"- $, .$&*-+ 3 J&(%,+ #$ (0-+ #$ ,+' '0(%0$&*$' ,+(+*0/+'@


38/46

36

H3:3'$-&",*

O-;-&"*$% KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

L$ ,,")" N-;-&"*$% #" *".&'- D < '%(:. P C#0'*0&*+ #$ .$-+D " ," *-"&'H+-)".0:& >%$ I".$ .+--$'/+$- " %& /%&*+ ) +*-+ )Q5 ",0&$"#+ .+& ) 3 D5 *", >%$K D)QRPD) 1 L0 PST '$ ,,")" N-;-&"*$% #$'"*&% 3 '0 PUT '$ ,,")" N-;-&"*$% $.+"',%7

)*&$+$#%# *-. /"-0"1'%2

2+&'*-%3$ $,

/$&*J(+&+

#$


39/46

37

)*&$+$#%#", 3%'% "4 %54%2

W1 2+&'*-%3$ $& c$+($9-" %& .%"#-0,J*$-+ .+)+ $, '0(%0$&*$K

"D 6/,G.",$ %&" I+)+*$.0" #$ -"4:& [ 3 .$&*-+ .%",>%0$- /%&*+ >%$ $,0B"'1

9D =2%J, $' ," -"4:& $&*-$ d6q 3 d6@

.D =j%? -$,".0:& $a0'*$ $&*-$ ," )$#0#" #$ ,+' ,"#+' #$ ")9+' /+,G(+&+'@

#D =2:)+ '+& ,+' J&(%,+' #$ ,"' #+' H0(%-"'@

$D =j%? -$,".0:& $a0'*$ $&*-$ ,+' /$-G)$*-+' #$ ")9"' H0(%-"'@

HD =j%? -$,".0:& $a0'*$ $&*-$ ,"' J-$"' #$ ")9"' H0(%-"'@


40/46

38

I(&,3,*

V-';%, #" @-.,&'5$' V'$,-,KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

)*&$+$#%#", *-. /"-0"1'%2

Fa0'*$& '0$*$ H+-)"' #$ .+&'*-%0- %& H-0'+ .+& ,+' )+%$ /%$#$' $&.+&*-"- $& ," 6,I")9-" 9%'." .%", $' $, /"*-:& )G&0)+ #$ -$/$*0.0:&5 )J-.",+ 3 #0 >%$ )+%$ *+#+ /%&*+ #$ ," -$(0:& E /$-*$&$.$ " %&" 3 ':,+ %&" #$ #0.I"' H0(%-"'1

!+' C'$,-, '+& .%9-0)0$&*+' #$ -$(0+&$' #$ ,+&(0*%# 0&H0&0*" /$-+ #$ "&.I%-" H0&0*"1 Q+- $,,+ ,"' ]&0."' 0'+)$*-G"' >%$ /%$#$& H+-)"- /"-*$ #$ $,,+' '+&K

• ,"' *-"',".0+&$' #$ %0#0'*" #$ ,+' 9+-#$' #$ ," -$(0:&1

• ,"' '0)$*-G"' .%3+ $B$ $' ," -$.*" >%$ $>%0#0'*" #$ ,+' 9+-#$' #$ ," -$(0:& + $' /$-/$.%,"- " #0.I" -$.*"1

• ,"' '0)$*-G"' $& #$',04")0$&*+ .%3+ $B$ $' ," -$.*" >%$ $>%0#0'*" #$ ,+' 9+-#$' #$ ," -$(0:&1


41/46

39

#3,"&-3, 7$56/"($, J G$:& ($56/"($,*

)*&$+$#%#", *-. /"-0"1'%2

6>%G *$&$)+' #+' #$ ,"' H+-)"' #$ .%9-0- $, /,"&+ .+& /+,G(+&+' -$(%,"-$'K

)*&$+$#%#", *-. /"-0"1'%2

2+&'*-%3$ $, .%9-0)0$&*+ #$, /,"&+ .+& $, I$aJ(+&+1

)*&$+$#%#", 3%'% "4 %54%2

67 Q"-" .%9-0- $, '%$,+ #$ ," .,"'$ .+& ,"' )0')"' ,+'"' .+& H+-)" #$ /+,G(+&+ -$(%,"-5 ':,+ /+#$)+' %'"- ,+'"' #$ *-$' H+-)"' #0'*0&*"'1 =j%? /+,G(+&+' /+#-J& '$- $'*"' ,+'"'@ =Q+- >%? &+ /+#$)+' %'"- +*-+' /+,G(+&+' -$(%,"-$'@

L$ ,,")" ;-,%$*- " *+#+ .%9-0)0$&*+ #$, /,"&+ )$#0"&*$ /0$4"' ,,")"#"' *$'$,"' >%$ &+ /%$#$& '%/$-/+&$-'$5 &0 /%$#$& #$B"- I%$.+' '0& -$.%9-0-1

Q+- *"&*+ ,+' J&(%,+' >%$ .+&.%--$& $& %&


42/46

40

F'*+' )+'"0.+' '$)0 -$(%,"-$' '+& ,+' '0(%0$&*$'K

F'*" '$-G" %&" #$ ,"' H+-)"' #$ .%9-0- $, /,"&+ .+& $'*+' )+'"0.+'K

)*&$+$#%#", *-. /"-0"1'%2

2+&'*-%3$ %&+ #$ ,+' "&*$-0+-$' .%9-0)0$&*+' #$, /,"&+ .+& )+'"0.+' '$)0-$(%,"-$'1

)*&$+$#%#", 3%'% "4 %54%2

67 P"4 %& )+'"0.+ '$)0 -$(%,"- " $'."," /"-" .%9-0- $, '%$,+ #$ %&" I"90*".0:& #$ ZaX )$*-+'

Z. 4-, ;-,%$*-, ,";$ '"054%'",\ $, )+*0%$ '%' ,"#+' .+0&.0#"&1 !" .+.0:& "


43/46

41

#3,"&-3, $2 /" K/L":B("*

E"( +-4%#-'KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

)*&$+$#%# *-. /"-0"1'%2

2-$" ," *$'$," s/$4


44/46

42

O5",-KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

L$ /%$#$ "M"#0- %& #$',04"#+- >%$ &+' /$-)0*" (0-"- #$ H+-)" (-"#%", %&" H0(%-"1

)*&$+$#%# *-. /"-0"1'%2

2+&'*-%3$ ," *$'$," sI%$'+t .+& "3%#" #$ c$+($9-"

)*&$+$#%# *-. /"-0"1'%

2+&'*-%3$ %& "


45/46

43

#3,"&-3, %$ A,-L$( MK:;/&"-&12N*

@-.,&'5**$:. X"3&$4", #" Z,*N"' I*-. 34%.&$44%HKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

F, +9B$*0


46/46

cuadernillo-geogebra

Documents