第三章位置与坐标(单元测试·拔尖卷)(原卷版)_2026语数英7-9年级上《举一反三系列》多版本_2026《初中数学•举一反三系列》8上多版本_2026《初中数学•举一反三系列》8上(北师大)

                                                                           
                                                                       
第三章  位置与坐标·拔尖卷
 2024

120      

120 

___________
___________	
___________
 !
" #$ 24 #%&' 10 #%() 6 #%*+ 8 #% 120 %, 120 %" #-./012%34
56%'#789%:;<=>?"@ABCDEFGH
IⅠ 
JK'L#M$ 10 N#% 30 %ON# 3 P
1KM3 PM24-25 QRS·TUVW·XYPZ[5\]^_`a%b(a,a−2)cxdCefg 1%haCi
gM    P
AK1
BK±1
CK1 j 3
DK2 j 3
2KM3 PM24-25 QRS·klmn·XaPobA(3,a)Zxdp%hbB(a−1,a+2)ZM    P
AKIJq,
BKIrq,
CKIsq,
DKITq,
3KM3 PM24-25 QRS·tuv·XYP[5\]^_`aCbP(m%1−2m)JwxZCq,yM    P
AKIJq,
BKIrq,
CKIsq,
DKITq,
4KM3 PZ[5\]^_`a%obA(a,−1)zbB(4,b){xd/|%hM   P
AKa=4%b=−1
BKa=−4%b=1
CKa=−4%b=−1
DKa=4%b=1
5KM3 PM24-25 QRS·}~€·XaPZ[5\]^_`a%‚AB∥yd%ƒbAC^_g
(m,2m−1)%bBC^_g(2,4)%hbAC„^_gM   P
AK4
BK3
CK0
DK−3
6KM3 PM24-25 QRS·…†‡ˆ·XYP‰Š%N‹ŒŽ{(3,0)%Ša‘’“”•‹%N
‹Z‹–pC—˜™š‰Š‘’K‰›N‹ŒŽ{(1,0)%œžŸC“”•‹%N‹I 1  ¡c‹
–¢%N‹CŽ£y(0,1)%¤¥N‹I 2025  ¡c‹–¢%N‹CŽ£yM   PK
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
AK(1,0)
BK(0,1)
CK(7,0)
DK(8,1)
7KM3 PM24-25 ¦RS·k§¨·XYP©ª«¬C­®%¯a°±²³´gµK‰Šy©ª«¬¶
·Š%o¸’¹Œº»CbC^_g(0,3)%¸’¼½¾¿CbC^_g(1,−3)%h¸’»À»CbC^
_gM   P
AK(2,−1)
BK(−1,2)
CK(1,2)
DK(−3,2)
8KM3 PM24-25 QRS·6ÁW½·XaP‰Š% Z[5\]^_`a% bA(2,3),B(−2,3),C(−2,−1),D
(2,−1) %b P Âb A ÃÄ%ÅOÆ 2 Ç&Ž«9CÈ9A→B→C→D→A¶ÉÊ˗˜%hI 2025 Æ
b P C^_yM       P
AK(0,3)
BK(2,1)
CK(−2,1)
DK(0,−1)
9KM3 PM24-25 QRS·ÌÍÎÏ·XaPwÐ
Ty[5\]^_`aCJbƒxZ^_dp%ÑbT
ҔxdÓydÔÕ·Ö%o×ØÕ·ÖC«9CÙg 4%hbTÚÔ“Õeb”%ۉ
ŠaCbP,Qy“Õ
eb”KoM(2m−5,11−3m)yITq,Cb%ƒbMy“Õeb”%hmCigM    P
教辅资源，关注公众号★全科AA+
教辅资源,关注公众号•全科AA+
                                                                           
                                                                       
AK2
BK4
CK
22
5
DK10
10KM3 PM24-25 QRS·6~lÀ·XYP‰Š%Z[5\]^_`a%7ÜÝ\]s]Þ△A1A2A3%
△A3A4A5%△A5A6A7%…%bA1(−2,0)%A2(−1,−1)%A3(0,0)%…%hßàŠ’áâ%bA1020C^_yM    P
AK(2,510)
BK(−5,−510)
CK(−2,510)
DK(−1,−510)
rK()#M$ 6 N#% 18 %ON# 3 P
11KM3 PM24-25 QRS·tuv·XaP“ãäp7 A%B ×b%oÅb A gžbåæ[5\]^_
`%hb B C^_g(2,−1)KoÅb B gžbåæ[5\]^_`%hb A C^_g        
K
12KM3 PM24-25 QRS·tçè·XaPZ[5\]^_`a%‚bP(−3,4)%«9g 3 C·ÖPQ
z x d[é%hb Q C^_y      
K
13KM3 PM24-25 QRS·tuv·XaPZ[5\]^_`a%bA(2−a,3a−8)c×Ø^_dCef
êÜ%h a Ciy          
K
14KM3 PM24-25 ëRS·½~쨷XaPDeepSeekíîZïÄJðñ{[5\]^_`SCòó
ôõKgöôõC÷ø0%ùúZ^_`aû£üÅSýb
A(1,6)¸’Œb%B(5,8)¸’þbK‰
›ôõÿĀZ·ÖABāû£JÇa³Ă%ƒa³ĂcbAÙbBCefêÜ%ha³ĂC^_g       
K
15KM3 PM24-25 QRS·½~pă·XaPZ[5\]^_`a%b A C^_g(m,n)%o m%n Ąg
ąĆ%ƒmn>0%m+n=4%hb A C^_:ćy          
K
教辅资源，关注公众号★全科AA+
教辅资源,关注公众号•全科AA+
                                                                           
                                                                       
16KM3 PM24-25 QRS·µĈĉW·ĊÖċČPZ[5\]^_`a%‚bMC^_g(2−t,2t)%č
bMcxdCefĎÔd1%cydCefĎÔd2K
M1Pot=4%hd1+d2=        
ď
M2PobMZIrq,%ƒmd1−4d2=8MmgĐĆP%hmCig
K
IⅡ 
sK*+#M$ 8 N#% 72 P
17KM6 P‚bP(2n+4,n−1)%ÒßàSđØõ%ĒÃb P C^_K
(1)b P C„^_ēĔ^_ 3ď
(2)b P Z y dpď
(3)b P ZÑbA(1,−2)ƒz x d[éC\·pK
18KM6 PM24-25 QRS·kĕĖ·XaP ‰Š%\]^_`a%△ABCCėbĄZĘãbp%ęa%
Cb^_g(1,2)K
(1)()
bAC^_y
%b B C^_y 
ď
(2)č△ABC̔ě[Ĝ2Ç&Ž«9%ĝ”p[Ĝ1Ç&Ž«9%Ğc△A′B′C′KğĠÃ△A′B′C′CsÇėb^
_ď
(3)Ē△ABCC5ġK
19KM8 PM24-25 QRS·½~lĢ·XaP/{[5\]^_`aCģĤJbP(x,y)%ĥÉSwÐ
bP1(x+1,2y−1)gPC 1 	Ħ=b%bP2(−y,−x)gPC 2 	Ħ=b%ۉP(2,3)C 1 	Ħ=bgP1(3,5)%ħC
2 	Ħ=bgP2(−3,−2)
(1)‚bP(2,4)%¤¥ħC 1 	Ħ=bg___________%2 	Ħ=bg___________ď
(2)očbPp[Ĝ 1 Ç&Ž«9%\ĨÒĠÃP1,P2[Ĝ“”Ùefď
(3)‚bP(−m,2m)ĩĨħC 1 	Ħ=bP1Ù 2 	Ħ=bP2%o·ÖP1P2é{^_d%ĒmiK
20KM8 PM24-25 QRS·Ī~īĬ·XaPĭĮNįİı®IJijYĴĵĶķéĸĹČĺ˜%Ã
ÄĻļļčĽÇĵĶCŽ£_Z‰Š‘’C[5\]^_`a%ęabA¸’“/ľĭĵĶ”CŽ£%^_
教辅资源，关注公众号★全科AA+
教辅资源,关注公众号•全科AA+
                                                                           
                                                                       
g(−1.3)%bB¸’“ĿĿŀĵĶ”CŽ£%^_g(2,2)K
(1)ßàÅp!%ğZ’ĤŠaŁÃļļåæC[5\]^_`K
(2)o“łľŀĵĶ”C^_g(0,−2)%ğZ[5\]^_`a_ÓłľŀĵĶ”CŽ£%Ń_bDK
(3)oļļZ_bCMŠa_P“ńŅņĵĶ”CŽ£%Ĕӄ^_Ňňü%hîøCbCʼnZI______
q,K
21KM10 PM24-25 QRS·tŊW·XYPZ[5\]^_`a%Oy^_žb%wÐbAÙbBC
ŋi[A,B]‰S
oO%A%BZJØ\·p%[A,B]=0ďoO%A%BxZJØ\·p%[A,B]=S△OABMƒS△OAB
>0PK‚bA^_g(4,0)bB^_g(0,4)%Ō+Sđō#
(1)[A,B]=_____ď
(2)o[P,A]=0%[P,B]=1%hbP^_g_____ď
(3)o[P,A]=2[P,B]%ƒbPC„^_g 2%ĒbPC^_ď
(4)obAÙbBCŋiŎ[P,A]=[P,B]%ğZ[5\]^_`aŁÃŎØõC‘7CbPÞİC¶ÉŠ
ÞK
22KM10 PM24-25 ¦Rp·µĈŏµ·XaP‰Š%Z[5\]^_`a%IJ č△OABŐőİ△OA1
B1%Ir č△OA1B1Őőİ△OA2B2%Is č△OA2B2Őőİ△OA3B3ŐőÑúaĽb^_Òg
A(1,3)%A1(2,3)%A2(4,3)%A3(8,3)%B(2,0)%B1(4,0)%B2(8,0)%B3(16,0)K
教辅资源，关注公众号★全科AA+
教辅资源,关注公众号•全科AA+
                                                                           
                                                                       
(1)ŒœO ŐőĻŔCs]Þ7ŕŐŖ%ŗÃáâ%Řáâĝč△OA3B3Őőİ△OA4B4%hA4C^_g
______%B4C^_g______%△OA4B4C5ġg______K
(2)Åpáâč△OABķé n  ŐőĞc△OAnBn%hAnC^_g______%BnC^_g______ď
(3)△OAnBnC5ġg______
23KM12 PM24-25 QRS·řÀŚś·XaPMŜŝŞČ·Ćz=床PßàšŢ%ţİĺ˜ģŤK
ťŦ“ŧaĽŽ£bC^_¸’
šŢJ
Ũũ%ŪūaŬŭŮůåŰ 70 ijRűĺ˜%QRCĆŜŝŞNįİıŲÑmųŴwķé“
ŧŐő¸ŵ%Ŷ 60 ŷŸz%įİ5×12C«“Þ“ŧŹOŷźJė©ŻCżľ%Žžſƀźp%ƁŔ%Ƃ
ÃåŰ“1945”“ŧď/ʼn 37 Žƃź©ŻżľĂæKęƄƃƅƆżľƇS%ƈƉ“ŧƊÞ 30 ÆŔ%
ŐőcƋZ“2025”“ŧď/ʼn 45 Žƃź©ŻżľĂæ%ęƄƃƅƆżľƇSK
šŢr
1945 “ŧŠ
*Ŵō#
ģŤJ
oƃACŽ£IJ^_¸’g(−4,1)%ƃBCŽ£IJ^_¸’g(−2,2)%ğåæŠƌC[5\]^
_`%ŃÒIJ^_¸’ÃƃCÓDÓECŽ£ď
ģŤr
‰›Z“1945”“ŧCñƍpŐőÓ2025”“ŧ%ĀĒŒæÙƇSŐőCƃƎ:ćƏ%ğZģŤJ
Cñƍp\ĨĠÃŐŖÑúaÿĀĂæÙƇSCƃ/ʼnCŽ£^_K
24KM12 PM24-25 QRS·ƐƑƒĢ·XaP‰Š 1%Z[5\]^_`a%·ÖABC×ÇƓb^_
ÒgA(0,2)%B(−1,0)%č·ÖAB”Ɣ[Ĝ 3 Ç&Ž«9%Ğc·ÖDC%ĩĨADK
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
(1)\ĨĠÃb CÓb D C^_K
(2)‰Š 2%ƕ«DCƖ y d{b E%b F y·ÖOEpCJǘb%ĩĨCFÓBF%ƗƘ∠ABFÓ∠BFCÓ∠ECF
āCĆ<`%ŃƙƚƛŶK
(3)Z^_dpyƜƝZb P ¯s]ÞPBDC5ġzT¢ÞABCDC5ġêÜƞoƝZ%ğ\ĨĠÃb P C
^_ďoxƝZ%ƙƚƛŶK
教辅资源，关注公众号★全科AA+