2025年新高考重难点13 极化恒等式与等和（高）线定理【四大题型】（解析版）.pdf

重难点13极化恒等式与等和（高）线定理【四大题型】

13

25

38

411

1

.

1

1

(1)

rrrrrr

2222

|a+b|+|a-b|=2(|a|+|b|).

uuurruuurruuurrruuurrr

AB=a,AD=bAC=a+bDB=a-b

uuur2uuur2rr2r2rrr2

AC=AC=a+b=a+2a×b+b



uuur2uuur2rr2r2rrr2

DB=DB=a-b=a-2a×b+b



uuur2uuur2r2r2uuur2uuur2

AC+DB=2a+b=2AB+AD.



(2)

1érr2rr2ùóóóó

a+b-a-b

êú

4ëû

rr1é22ù.

a×b=4ëAC-DBû

2ìîìî

1

4

(1)ìîì

î11érr2rr2ù().

a+b-a-b

êú

44ëû

(2)

(MBC)().

.

2()

1()

(1)()(λ,μ∈R)

λ+μ=1△OAB△OABk,k∈R

(x,y∈R)∴x+y=kλ+kμ=k.

(2)(λ,μ∈R)PAB

ABλ+μ=k()ABAB()

.

①ABk=1

②OABk∈(0,1)

③ABOk∈(1,+)

④Ok=0

⑤Okk

12

⑥kO.

1

△

12024DEF

⋅=7⋅=2⋅=

A−2B−1C1D2

,,,,⋅⋅,