第三章位置与坐标(讲义)(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（举一反三讲义）全章题型归纳
 2024
 ...................................................................................................................................................................3
 1   !" ............................................................................................................................3
 2  #$%& ............................................................................................................................3
 3  '()*% ................................................................................................................3
 4  +,-./012 ........................................................................................................................4 
 5  34567 ............................................................................................................................5
89 ...................................................................................................................................................................6
 6  :/;<=>? ....................................................................................................................6
 7  :,-@A<=>? ....................................................................................................................7
 8  34;7>? ....................................................................................................................9
 9  34BC37>? ..............................................................................................................11
知识点1  有序数对的概念
DEFGHIJKL ɑ : b MNL1OPQGIL1ORS(𝑎O𝑏)T
知识点2  平面直角坐标系及有关概念
1. .5UB3
V.5WOJXYZ[U0\]^L(OMN.5UB3T_`JXL(abcde.fcgh
UfcOijk:jlmjabnJXL(omjT
2. (
e.L(2n x (+p(OhUL(2n y (+q(Trst2n(OJ(u O 2n.
5UB3\T
3. !"
.5vJX(aNwKxa
klxaPQyz!"O{|}Kxa~€mjabPQyr
!"0y}!"0yw!".T
知识点3  建立平面直角坐标系
1. ‚ƒ.5UB3„…
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‡aˆX‰OŠ‹ŒSn\Ž
†2‡\VJKYZ[UmjlabS x (0y (Ž
†3‡‘’omjg“f”CT
2. `•‚ƒ3m–
—˜™}B-š›4n\Oš›œš›lžVUŸn(T
知识点4  平面直角坐标系内点的坐标
1.  ¡
.5W¢—£zKGIL1¤ ¡T1d.5W¥¦z PO P abj x (0y (S[ŸO[§
V x (0y (l1¨©L a,b abPQ P p0qOGIL1(𝑎O𝑏) ªPQ P . 
.5W:GI©L1«zz1¨T
2. ¬­¦®
†1‡ P(𝑎O𝑏)' x ()*n|𝒃|Ž†2‡ P(𝑎O𝑏)' y ()*n|𝒂|T
3. #$
†1‡¯!"W#$
yz°yw!"W±	²³n( + O + )0(−O + )0(−O−)0( +
O−)T
†2‡´!"W#$
x (lqn 0Žy (lpn 0Ž\p0q
µn 0Ž\¶V x (lO·V y (lT
†3‡:(.¸UŸl#$
: x (.¸UŸlžGqZ¹O: y (.¸
UŸlžGpZ¹T
知识点5  用坐标表示平移
†1‡./
./º»@¼<=
V.5UB4O½(xOy)jk(+¾)./ a K“f
”CO¢—¿'1¨(x+aOy)+(x-aOy)Ž½(xOy)jl(+À)./ b K“f”CO¢—¿'1¨(xO
y+b)+(xOy-b)T
†2‡,-./
V.5UB3WOÁÂFzK,-¯KpµÃ(+ÄÅ)zKoL aOZ¨
Æ,-ª«F\,-jk(+j¾)./ a K“f”CŽÁÂFǯKqµÃ(+ÄÅ)zKoL
aOZ¨Æ,-ª«F\,-jl(+jÀ)./ a K“f”CT
知识点6  轴对称与坐标变化
†1‡d x (12JKOpZ¹OqYnZÈL;ȏ¤OpZ¹0qYnZ
ÈLJKd x (12T
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
†2‡d y (12JKOqZ¹OpYnZÈL;ȏ¤OqZ¹0pYnZ
ÈLJKd y (12T
【培优篇】
【题型1  由点的坐标判断象限】
É 1Á,«Ê;ËÌ.5¡¦,O͗În\Ojkmjn𝑥(omjOjlmjn𝑦(om
j‚ƒ.5UB3OÏÐўV!"«(        )
ATyz!"
BTyr!"
CTy}!"
DTyw!"
@– 1-1†24-25 ÒÓÔÀ·]Õ·ÖׇV.5UB34O(2025,2025)žV!"«†   ‡
ATyz!"
BTyr!"
CTy}!"
DTyw!"
@– 1-2†24-25 ØÓÔÀ·ÙÚÛÜ·Ö4‡V.5UB34O𝑃(−𝑎2−1,3)žV!"«†Ý݇
ATyz!"
BTyr!"
CTy}!"
DTyw!"
@– 1-3†24-25 ØÓÔÀ·Þß·Ö4‡V.5UB3𝑥𝑂𝑦4O𝐴(𝑥,𝑥+ 1)z’àVy          
!"T
【题型2  由点的坐标特征求值】
É 2†24-25 ØÓÔÀ·]ÕáÚ·Ö4‡V.5UB34OÍ𝐴(𝑛−2,7)V𝑦(lOÏ𝐵(𝑛−3,𝑛+ 1)
Vy        
!"T
@– 2-1†2025·Ùâã·äåæç‡Íyr!"W𝑃(𝑚,𝑛)è§𝑛−𝑚= 2OézKè§X‰𝑃

        
T
@– 2-2†24-25 ØÓÔÀ·êڔë·Öׇìí.5UB34GJ𝑀(2𝑚−3,𝑚+ 1)0𝑁(−5,−1)O
î𝑀𝑁∥𝑥(€OÏ𝑚=         
T
@– 2-3†24-25 ÒÓÔÀ·Ùïð·Ö4‡V.5UB34Oìí𝑃(𝑎,𝑎+ 1)O𝑄(−1,2)TÍUŸ
𝑃𝑄:𝑥(.¸OÏ𝑎&n     T
【题型3  由点到坐标轴的距离求坐标】
É 3†24-25 ØÓÔÀ·Ùñò·óôõö‡𝐴(2,𝑚)Vyw!"Oî'JX()*÷gn 5OÏ
𝐴n        
T
教辅资源，关注公众号★全科AA+
@– 3-1†24-25 ÒÓÔl·øù·“úçû‡ìí𝐴(3𝑎,2𝑏)V𝑥(lmOV𝑦(¾üOÏ𝐴'𝑥(0𝑦(
)*abn†    ‡
AT3𝑎,−2𝑏
BT−3𝑎,2𝑏
CT2𝑏,−3𝑎
DT−2𝑏,3𝑎
@– 3-2ìí𝑃(𝑎,𝑏)Vyw!"Oî P ' x ()*n 5O' y ()*n 3OÏ P 
n            
 T
@– 3-3†24-25 ÒÓÔl·ýþýÕ·ÖׇV.5UB34Oìí A n(2−𝑎,2𝑎)OF A
' x ()*RS mO' y ()*RS nT
(1)Í𝑎= 5O%𝑚𝑛&Ž
(2)Í𝑎> 2,𝑚+ 𝑛= 7O% A T
【题型4  点或图形的平移、对称】
É 4†24-25 ØÓÔÀ·ÿĀāã·ÖׇÁ,OÍVĂăl‚ƒ.5UB3OĄ“ą”fd(2,0)OÏ
½ĂĆ“ć”jl./ 2 K“f”CĈ«      
T
@– 4-1†24-25 ĉÓÔl·ĊċċĀ·ÖׇV.5UB34O𝐴(−2,1)d\12 B Vy      
!"T
@– 4-2†24-25 ÒÓÔÀ·]Õ·Ö4‡V.5UB34OÍ𝐴(−7,6):𝐵(𝑎,𝑏)d𝑥(12OÏ
𝑎+ 𝑏=           
T
@– 4-3†24-25 ØÓÔÀ·Č‚čηÖׇV.5UB34ORpqµ«ĎLnĎT½
zKĎďĐ¥z(mj./ 2 K“fOđĐ:Ēz³./[Umj./ 1 K“fOPQz³ “ēć
Ĕ;”TÉÁ∶Á,O A Qz³“ēćĔ;”O¢—'ĕ BOĖ«'ĕàė CT P Ę\ęĚěQ“ē
ćĔ;”OÀ5}KĜĝ4OžGo‘ĜĝI	«                  
T
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 P иz³“ēćĔ;”¢ğ'ĕG 8 KŽ
② P и}³“ēćĔ;”Ĉ¢—'ĕ(1,0)Ž
③ P иw³“ēćĔ;”Ĉ¢—'ĕ(0,3)T
【题型5  坐标系中的面积问题】
É 5†24-25 ØÓÔÀ·êĠġ·óôõö‡Á,OV.5UB34O”m-𝐴𝐵𝐶𝑂”𝐴𝑂n4OĢ𝐴𝐵
n3O;𝑃Ę𝐴ģĐ𝐴𝐵→𝐵𝐶→𝐶𝑂Ĕ;O △𝑃𝑂𝐴56˜dw›-𝐴𝐵𝐶𝑂56
1
6€O𝑃
n          
T
@– 5-1†24-25 ÒÓÔl·ðĀĊĤ·Ö4‡VÁ,ž¡UB34Ow›-𝐴𝐵𝐶𝐷¯Kĥ
ab«𝐴(0,2)O𝐵(5,5)O𝐶(8,0)O𝐷(2,−2)OÏĦKw›-56«      
T
@– 5-2V.5UB3𝑥𝑂𝑦4O1d¥¦}𝐴O𝐵O𝐶“ħ56”OĨÁÀ’®
“e.š”𝑎
¥
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
¦JpĩĪ&O“ī[”ℎ
¥¦JqĩĪ&OÏ“ħ56”𝑆= 𝑎ℎTÉÁ
}
abn𝐴(1,2)O𝐵(−3,1)O𝐶(2,−2)OÏ“e.š”𝑎= 5O“ī[”ℎ= 4O“ħ56”𝑆= 𝑎ℎ= 20TÍ𝐷(1,2)O
𝐸(−2,1)O𝐹(0,𝑡)}“ħ56”n18OÏ𝑡&n†    ‡
AT−3+7
BT−4+6
CT−4+7
DT−3+6
@– 5-3†24-25 ØÓÔÀ·WĬĭĮįİı·Ö4‡Á,OV.5UB34Oìí𝐴(𝑎,0)O𝐵(𝑏,0)O
{4 aOb è§|𝑎+ 1| + (𝑏−3)2 = 0T M (−2,−1)OV y (oIJ(lGz POĄ¿ △𝐵𝑀𝑃5
6: △𝐴𝐵𝑀56Z˜OÏ P n†  ‡
AT(2,0)
BT 0,
2
5
CT 0,
1
5
DT 0,
3
4
【拔尖篇】
【题型6  坐标与点的移动规律探究】
É 6†24-25 ØÓÔÀ·ÿijÚĴ·ÖׇÁ,OV.5UB34O A Ę\ O ģOĐ x (om
j~IJĵ-ĶŸà jĒĔ;O{/;ķŸÁ,ž¡O{4IJĵIJĸn 1 K“f”COĦ€𝐴1O𝐴2O
𝐴3O𝐴4…abn𝐴1(0,0)O𝐴2(1,1)O𝐴3(2,0)O𝐴4(3,−1)…O~ĹĦĺ<=ÀÅO𝐴2025
n      
T
@– 6-1†24-25 ÒÓÔÀ·ĻijÚÜ·ÖׇÁ,OļĽ»ě€fd(3,0)ęOĐ,4ž¡mjľĽOļĽ
VĽĿlĔ;ŀŁÁ,ž¡TÁÂļĽ»ě€fd(2,0)ęOł~\¤mjľĽOļĽy 1 ³Ń'ĽĿ
›€OļĽfc«(0,2) OńŅļĽy 2025 ³Ń'ĽĿ›€OļĽfc«†Ý݇
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
AT(2,4) 
BT(6,0)
CT(8,2)
DT(6,4)
@– 6-2†24-25 ØÓÔÀ·ņŇĻ·óôõö‡Á,Oìí𝐴1(1,1)O𝐴2(2,−1)O𝐴3(4,4)O𝐴4(6,−4)O𝐴5(7,1)
O𝐴6(8,−1)O𝐴7(10,4)O𝐴8(12,−4)⋯⋯O~Ħĺ<=OÏ𝐴2025n†Ý݇
AT(3038,−1) 
BT(3037,−1)
CT(3037,1)
DT(3038,1)
@– 6-3†24-25 ĉÓÔÀ·ňĴʼnH·óôõö‡Á,OV.5UB34O”m-𝐴𝐵𝐶𝐷wKĥ
abn𝐴−1O2 O𝐵−1O−1 O𝐶(1,−1)O𝐷(1,2)𝑃Ę𝐴ģOДm-𝐴𝐵𝐶𝐷›H€Ĕ;OŊ
CnŋŌ 2 K“f”CO𝑄Ę𝐴ģOДm-𝐴𝐵𝐶𝐷›€Ĕ;OŊCnŋŌ 3 K“f”COR
𝑃O𝑄V”m-𝐴𝐵𝐶𝐷›ly 1 ³Zō€n𝑀1Oyr³Zō€n𝑀2Oy}³Zō€n𝑀3O
⋯⋯OÏ𝑀2025n†    ‡
AT(1,0)
BT(−1,0)
CT(−1,2)
DT(0,−1)
【题型7  坐标与图形变换规律探究】
É 7†24-25 ÒÓÔÀ·ðĀŎŏ·óôõö‡Á,OVUB34OŋKŐőļom-›”Œn 1 K
“f”CO—𝑃nĥSom-𝑃𝐴1𝐴2𝐴3Oom-𝑃𝐴4𝐴5𝐴6O…O~œ<=SÀÅOžSom-ĥŒ
教辅资源，关注公众号★全科AA+
VőlO{4om-𝑃𝐴1𝐴2𝐴3ĥabn𝑃(−3,0)O𝐴1(−2,1)O𝐴2(−1,0)O𝐴3(−2,−1)OÏĥ𝐴100
n            
T
@– 7-1†24-25 ÒÓÔÀ·ÙÚ.ĥð·Ö4‡Á,OV.5UB34O △𝐴1𝐴2𝐴3O △𝐴3𝐴4𝐴5O △
𝐴5𝐴6𝐴7O △𝐴7𝐴8𝐴9O⋯µ«˜›}B-Oî𝐴1O𝐴3O𝐴5O𝐴7O𝐴9ab« 𝐴1(3,0)O𝐴3(2,0)O 𝐴5
(4,0)O𝐴7(1,0)O𝐴9(5,0)T²Ŕ,-žÈŕ<=OÏ𝐴2025«(   )
AT(509,0)
BT(508,0)
CT(−509,0)
DT(−505,0)
@– 7-2†2025 ÒÓÔl·øù·Ŗõö‡ÁÀ,OV.5UB34Oyz³½}B-𝑂𝐴𝐵@AN
}B-𝑂𝐴1𝐵1Oyr³½}B-𝑂𝐴1𝐵1@AN}B-𝑂𝐴2𝐵2Oy}³½}B-𝑂𝐴2𝐵2@AN}B-𝑂𝐴3𝐵3
,⋯⋯O²œ@AÀÅTìí𝐴(1,3),𝐴1(2,3),𝐴2(4,3),𝐴3(8,3),𝐵(2,0),𝐵1(4,0),𝐵2(8,0),𝐵3(16,0)T
(1)%}B-𝑂𝐴4𝐵4¯KĥT
(2)~œ,-@¼<=OŗŘ%}B-𝑂𝐴𝑛𝐵𝑛56:}B-𝑂𝐴𝐵56ļ3T
@– 7-3Á,OV.5UB3𝑥𝑂𝑦4O𝐴1(1,0)O𝐴2(3,0)O𝐴3(6,0)O𝐴4(10,0)O…O—𝐴1𝐴2n1B
教辅资源，关注公众号★全科AA+
ŸSyzKom-𝐴1𝐶1𝐴2𝐵1O—𝐴2𝐴3n1BŸSyrKom-𝐴2𝐶2𝐴3𝐵2O—𝐴3𝐴4n1BŸSy}Kom
-𝐴3𝐶3𝐴4𝐵3…ĥ𝐵1O𝐵2O𝐵3O…µVyz!"O~ĹĦĺ<=²³Ğ¸ÀÅO𝐵𝑛n          
T
  
【题型8  坐标系中的动点问题探究】
É 8†24-25 ØÓÔÀ·Þß·ÖׇÁ,OV.5UB34O”m-𝑂𝐴𝐵𝐶›𝑂𝐶0𝑂𝐴abV x (0y
(lOB Vyz!"O A «(0,4)O𝑂𝐶= 8T
(1)Uřé B0 C T
(2) P Ę\ O ģOV›𝑂𝐶l—ŋŌ 1 K“f”CŊCŚŊj C Ĕ;O¹€ Q Ę B ģOV
›𝐵𝐴l—ŋŌ 2 K“f”CŊCŚŊj A Ĕ;OzK'ĕś€OŜzKŝ÷ŞşĔ;OŠĔ
;€šn t ŌO>?ÀŢ7 
① t nţŤ€OUŸ𝑃𝑄∥𝑦(ť
②VĔ;Ŧ4O Q ' y ()*n 2 K“f”C€O% P0Q JT
③VĎKĔ;Ŧ4OğŧĄ¿w›-𝐵𝐶𝑃𝑄56«”m-𝑂𝐴𝐵𝐶56
5
8ťÍğOŗUřé P0Q J
ŽÍàğOŨũŪT
@– 8-1Á, 1OìíO𝐴(1,4)O𝐴𝐻⊥𝑥(O[§n𝐻O½Ÿô𝐴𝑂./°Ÿô𝐵𝐶O𝐵(3,0)O{4𝐴
:𝐵1¨O𝑂:𝐶1¨T
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)}B-𝐴𝑂𝐻56n__________T
(2)Á, 1OÍ𝐷(𝑚,𝑛)VŸô𝑂𝐴lOŗŘūř𝐷𝐻OŬ£,-563Ũũ𝑛= 4𝑚T
(3)Á, 2Oū𝑂𝐶O;𝑃Ę𝐵ĚěV𝑥(l—ŋŌ 2 K“fŊCj¾Ĕ;O¹€𝑄Ę𝑂ĚěV𝑦(l—
ŋŌ 1 K“fŊCjÀĔ;TÍŭ𝑡ŌO}B-𝐴𝑂𝑃:}B-𝐶𝑂𝑄56Z˜Oû%𝑡&œ𝑃T
@– 8-2†24-25 ØÓÔÀ·]ÕĻŮ·ÖׇÁ,OV.5UB34O𝐴𝐵∥𝐶𝐷∥𝑥(O𝐵𝐶∥𝐷𝐸∥𝑦(O
î𝐴𝐵= 𝐶𝐷= 3,𝑂𝐴= 4,𝐷𝐸= 2O; P Ę A ģO—ŋŌ 1 K“f”CŊCOĐ𝐴→𝐵→𝐶ķŸj C
Ĕ;Ž; Q Ę O ģO—ŋŌ 2 K“f”CŊCOĐķŸ𝑂→𝐸→𝐷j D Ĕ;TÍ POQ J¹€
ģO{4z'ĕś€OJµŞşĔ;T
 
(1)Uřé BOCOD }KŽ
(2) POQ Jģ2s€O%}B-𝑂𝑃𝑄56Ž
(3)Š POQ JĔ;€šn𝑡sO}B-𝑂𝑃𝑄56n 6 €O% t &T
@– 8-3ůzů
L-Ĝ^SnzŰLűŲmųO{¨£Ŵ·¢anJŰŵ-
+sŶŷdLŸ‘Ź¤źũ-ÊŻ
żŹO+sŶŷ-¬­UŽŹ¤źũL÷šÊŰ3OžL-Ĝ^ſƀJKm5
yzŰŵ-«“—LƁ
-”OƂyrŰŵ-«“—-ŷL”TÉÁ
VDEöL(€ƃOL(l¥¦JO𝐴 ¡Ln𝑎O𝐵 
¡Ln𝑏OÏ𝐴O𝐵J)*¢£–Ć|𝑎−𝑏| ¡OÉÁ
5 gƄ2 )*¢£|5−(−2)|+|−2−5| ¡T
ƅzƅ
Á,OV.5UB34OUŸ𝐴𝐵ab:𝑥(oIJ(0𝑦(oIJ(ud𝐴(𝑎,0)0𝐵(0,𝑏)Oî𝑎0𝑏è§
(𝑎−6)2 + |𝑏−4| = 0T
教辅资源，关注公众号★全科AA+
                                                                           
                                                                       
(1)Uř鐗À
𝐴†______O0‡O𝐵†0O______‡T
(2)Í𝑃0𝑄ab«𝑦(oIJ(†à:𝐵]^‡0𝑥(ƆIJ(l;O𝑄S𝑄𝐶∥𝐴𝐵Oūř𝑃𝑄Tìí
∠𝐵𝐴𝑂= 34°†Ƈƈ&‡Oŗ>Ɖ∠𝐵𝑃𝑄:∠𝑃𝑄𝐶÷šLƊ3OƋŨũŪT
(3)ìí𝐷(3,2)«Ÿô𝐴𝐵4OÍ𝐻n𝑦(lzOî𝑆△𝐴𝐻𝐷=
2
3𝑆△𝐴𝑂𝐵O%𝐻T
【题型9  坐标系中角度关系问题探究】
É 9V.5UB34O A0B abV x (0y (oIJ(lO𝑂𝐴:𝑂𝐵= 5:4O △𝐴𝑂𝐵56n 10O
𝐶(𝑚,4)Vyr!"O P «ƌŸ CB lz;O∠𝐶= ∠𝑂𝐴𝐵T
(1)% B Ž
(2)Ÿô OC ğŧ_./ AB ¿'ťû% C Ž
(3)∠𝑂𝑃𝐴0∠𝑃𝑂𝐶0∠𝑃𝐴𝐵÷šG­3ťŗŨũŪT
@– 9-1ÊƍиƎƏƐƑƒO½ƓaN 5 KöļMOƔiƕƕm–TÁ,ž¡OĦ«ÊƖ
Ò(1)ƗƐƘƙ,O𝐴0𝐵0𝐶0𝐷0𝐸abƚ ƛKöļMfcTìí𝐴n(-1O3)T
教辅资源，关注公众号★全科AA+
  
(1)ŗ~¦‚ƒ.5UB3†p(gq(Œnļom-›žVUŸOŋKļom-›”n 1 K“f
”C‡Oé,4{|¬KöļMŽ
(2)Í(1)4‚ƒ.5UB3\n𝑂O𝐹V𝐷𝐵Ɯ”ŸlOŗé∠𝐹𝐴𝐵0∠𝐴𝐹𝑂0∠𝐹𝑂𝐷÷š
˜Ɗ3OƋŨũ\ƝT
@– 9-2†24-25 ØÓÔÀ·ňĴăƞ·óôõö‡Á,OV.5UB34Oìí △𝐴𝐵𝐶O A 
«(4,0)O B «(2,3)O C V x (ƆIJ(lOî𝐴𝐶= 6T
(1)é C  Ž
(2)V y (l«ŧƟV POĄ¿}B-𝑃𝑂𝐵56˜d}B-𝐴𝐵𝐶56
2
3OÍƟVO% P ŽÍ
àƟVOŗŨũŪŽ
(3)F C Ơl./ 3 K“f¿' HOSƌŸ𝐶𝐻Oūř𝐵𝐻O M VƌŸ𝐶𝐻lĔ;†à: C0H ]
^‡OŗUřé∠𝐵𝑀𝐴O∠𝐻𝐵𝑀O∠𝑀𝐴𝐶÷šLƊ3T
@– 9-3Á, 1OV”m-𝑂𝐴𝐵𝐶4O𝑂n.5UB3\O𝑂𝐴= 2O𝑂𝐶= 4O𝐵Vyz!"T
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)𝐵n______Ž
(2)Á, 2O𝑃«Ÿô𝐶𝐵Ɯ”ŸlOūř𝐴𝑃O𝑂𝑃OÏ∠𝑃𝑂𝐶O∠𝐴𝑃𝑂O∠𝑃𝐴𝐵}KBè§3«ơ
ŅťƋŨũŪŽ
(3)V†2‡ƢƣlOìí
∠𝑃𝐴𝐵= 20°O∠𝑃𝑂𝐶= 50°OVyz!"Wiz𝐹Oūř𝑂𝐹O𝐴𝐹Oè§
∠𝑃𝐴𝐵= 2∠𝐹𝐴𝑃O∠𝑃𝑂𝐶= 2∠𝐹𝑂𝑃OŗUřé
∠𝐴𝑃𝑂
∠𝐴𝐹𝑂&T
教辅资源，关注公众号★全科AA+