B ................................................... B ..................................................................................... olan eksene .....(................................. B .......................... olan eksene .....(..............

Simedy an A kademi ... ... ... ... ... B ... olan eksene ... (... ... olan eksene ... (... B ... ... B ...

Simedy an A kademi B ` ... ` ... B ` ... ` ...

Simedy

an A

kademi

Örnek-1

Simedy

an A

kademi

Simedy

an A

kademi

Örnek-3

Simedy

an A

kademi

Örnek-4

Simedy

an A

kademi

Simedy an A kademi Örnek-6 A(a.b, a b4 ) göre, B(a.b2

Simedy

an A

kademi

Örnek-7

Simedy an A kademi Örnek-8 M K

Simedy an A kademi Örnek-9

.

Simedy an A kademi Örnek-10

x

y

A(0, 7)

C(6, 0)

B(5, 5)

O

Simedy an A kademi Örnek-11 x D C B(0, -3) A(4, 0) y _{ABCD kare} göre,

Simedy an A kademi 1 , y1) ve B(x2 , y2 ... ... ...

Simedy an A kademi x y y₂ y₁ x x B A H ... ... ... ... |AB| = ... |AB|= ...

B Özel olarak, A(x₁ , y₁

|AO|=...

Simedy

an A

kademi

Simedy

an A

kademi

Örnek-13

Simedy

an A

kademi

Örnek-14

Simedy

an A

kademi

Örnek-15

Simedy an A kademi Örnek-16 x A B C(3, 4) y O

Simedy an A kademi Örnek-17

D

E

B

A

C

Simedy

an A

kademi

A(2, 5), B(-1, 2), C(-2, -3), D(1, -3), E(2, 0), F(0, 3), G(-3, 0), H(0, -1)

Simedy

an A

kademi

Simedy

an A

kademi

göre,

Simedy

an A

kademi

4.

Simedy

an A

kademi

5.

Simedy an A kademi 6.

A(a+b, a.b

B(b-a, a.b)

Simedy

an A

kademi

7.

Simedy an A kademi 8.

B

A

Simedy an A kademi 9.

.

Simedy an A kademi

x

y

A(0, 3)

C(5, 0)

B(3, 4)

O

Simedy an A kademi

C

y

x

D(-4, 0)

A(0, -6)

B

[AB]

^ [AD]

[AB]

^ [BC]

A(0, -6) ve D(-4, 0)

Simedy

an A

kademi

Simedy

an A

kademi

ñ

Simedy

an A

kademi

göre,

Simedy

an A

kademi

Simedy an A kademi

x

A

D

B

C

y

O

Simedy

an A

kademi

Simedy an A kademi 1 , y1) ve B(x2 , y2 C Î [AB] ve |CA|_{|CB| = k} ... ... böler. Buna göre, x = ..._... ve y = ..._...

Simedy an A kademi PATLAYALIM A C H B G y x₁ y₁ y y₂ x x₂ x , y₁), B(x₂ , y₂ |CA| |CB| ... ... = ... olur. Buradan ... = ... ... = ..._... ... ... = ... ... = ... ... = ..._...

Simedy

an A

kademi

Simedy an A kademi Örnek-18

C

Î [AB] ve

|CA|

|CB|

= 3

₄

Simedy an A kademi Örnek-19

A(-1, 2)

C(x, y)

B(9, -3)

3.|AC| = 2.|BC|

Simedy an A kademi Örnek-20

D

B(-5, -2)

A

C(9, 5)

3.|AB| = 4.|AC|

-Simedy an A kademi 1

, y

) ve B(x

, y

C

Ï [AB] ve

|CA|

_|CB|

= k

...

...

böler.

...

=

...

_...

ve

...

=

...

_...

Simedy an A kademi PATLAYALIM 1 , y1), B(x2 , y2 |CA| |CB| ¿EC~B¿ ... ... = ... = ... olur. Buradan ... = ..._... ... = ..._... |CA| |CB| = |CE||CF| ... = ... ... ... = ..._... bulunur.

Simedy

an A

kademi

Simedy an A kademi Örnek-21

|CA|

|CB|

= 5

Simedy an A kademi Örnek-22

A(-3, 2)

B(0, 4)

C(x, y)

2.|CA| = 3.|CB|

Simedy

an A

kademi

Simedy

an A

kademi

1

, y

) ve B(x

, y

Simedy an A kademi PATLAYALIM A(x₁ , y₁) ve B(x₂ , y₂ x₁ y₁ x₂ x D G H K E C B F y y₂ A ` ... y = |AD| + |BF|<sub>2</sub> = ...<sub>...</sub> ` ... x = |AG| + |KB|₂ = ..._...

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi Örnek-26

x

E

C(5, 0)

A(2, 9)

B(-2, 1)

D

|AD| = |BD|

2.|AE| = |EC|

A(2, 9), B(-2, 1) ve C(5, 0)

Simedy

an A

kademi

Simedy an A kademi 1 , y1), B(x2 , y2) ve C(x₃ , y₃ E C D A B S S G F x = ..._... ve y = ..._...

Simedy

an A

kademi

Simedy an A kademi Örnek-29 E(-1, 3) F(3, 4) G(1, 2) C A S S göre,

B

Simedy an A kademi Örnek-30 G₁ 2 |G₁G₂

G

Simedy an A kademi NOT ..., ..., ... ve ... ... ... ... ... ... C(x₃, y₃) D(x₄, y₄) A(x₁, y₁)B (x₂, y₂) O ... = ... ...= ...

Simedy

an A

kademi Örnek-31

Simedy an A kademi Örnek-32

A(4, 6)

B

y

x

C

D(0, -2)

Simedy an A kademi

C

Î [AB] ve

|CA|

|CB|

=

3

₂

Simedy an A kademi C(6, 2) B(4, 0) x y A O [OA] ^ [AC] [BC] = 2.|AB|

göre, A(O¿AB) kaç br2

Simedy an A kademi

|CA|

|CB|

=

5

2

Simedy

an A

kademi

A(1, -3)B

(3, 1)

C(x, y)

Simedy an A kademi

A

B

|AB|

|AC|

=

2

₃

B(-2, 3) ve D(2,1)

C

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi

C

A

E

B

>

[DE] // [BC]

A(4, 7), E(5, 3) ve B(2, -1)

>

Simedy

an A

kademi

Simedy

an A

kademi

A(-1, 3), B(4, 2) ve C(6, -2) olan

Simedy an A kademi C(2, 3) B(4, 1) A G 11.

Simedy an A kademi

G

göre, |G

G

Simedy an A kademi

D(-1, -2)

A(1, 3)

_{B(4, 5)}

E

C

2.|EC| = |DE|

Simedy an A kademi

E

Simedy an A kademi I. _y d x d do rusunun e ... ve a e, do runun e ... m = ... II. _y x d .... d do rusunun e ... ve a e, do runun e ... m = ...

Simedy an A kademi III. _y x d d ^ ... m = ... IV. _{y d} x d ^ ... m = ...

Simedy an A kademi Örnek-33

y

120

₃₀

O

x

d

d

ve d

Simedy an A kademi Örnek-34 x m = y 3 1 m = x y -3 2 x m = y 2 -2

Simedy

an A

kademi

k

runun E

A x₁ , y₁) ve B(x₂ , y₂) noktalar çen

do runun e à olmak üzere, bu do runun e

m = tanà = ..._... r. x₁ y₁ x₂ B A y₂ .... ... ... .... ... ... ... ...

Simedy

an A

kademi

Simedy an A kademi Örnek-36

1

2

Simedy

an A

kademi

Örnek-37

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi Örnek-41

A

-3

B

y

d

x

C

O

2.|OA| = 3.|OB|

C(2m+1, 3)

Simedy an A kademi Örnek-42 y x A(5, 7) B(1, -4) C(x, 0) en az

Simedy an A kademi

`

m

= -

...

...

`

...

...

`

Simedy an A kademi Örnek-43 a) b)

c)

d)

e) y =

2x + 3

5

Simedy an A kademi Örnek-44

(a+3)x + (2a+1)y + 3 = 0

1

3

Simedy an A kademi A(x₁ , y₁ ... = ... . (...) formülüyle bulunur.

Simedy an A kademi PATLAYALIM x₁ ... ... y₁ x P A y .... ....

à olan d do rusu üzer ₁ , y₁) ve P(x , y) noktalar ver ... = ... = ..._... r. Buradan ... = ... . ( ... r. ... ... ... ...

Simedy

an A

kademi

Simedy an A kademi Örnek-46

2

3

Simedy an A kademi Örnek-47 B C(2, 3) y x göre,

Simedy

an A

kademi

Simedy an A kademi 1

, y

) ve B(x

, y

...

...

=

...

...

Simedy an A kademi PATLAYALIM 1 , y1) ve B(x2 , y2 ... olsun. y x y₁ y₂ x y x A B P x a ... ... = ... ... ... = ..._...

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi Örnek-51

y

B

A

O

C

d

D(16, 0) x

Simedy an A kademi Örnek-52 y A B D C x y= 23 x 2 3 k + m = 14

Simedy an A kademi Örnek-53 y C E x A G D(9, 0) O

OABC, ADEG ve GEFB

Simedy an A kademi b a y x ... ... + ...

Simedy

an A

kademi

Örnek-54

Simedy an A kademi Örnek-55

y

x

Simedy an A kademi Örnek-56 3x + 2y - 6 = 0 2

Simedy an A kademi y x y=x y=2x y=-x y=-2x ... ` ... ` ...

Simedy

an A

kademi

Örnek-57

Simedy

an A

kademi

Örnek-58

Simedy

an A

kademi

Örnek-59

Simedy

an A

kademi

Simedy an A kademi ` ax + b = 0 (ax + b = 0 x = - b a ) ` ay + b = 0 (ay + b = 0 y = - b a )

Simedy

an A

kademi

Örnek-61

Simedy an A kademi Örnek-62

x = -2 ve y = 5

Simedy an A kademi Örnek-63 x 2

Simedy an A kademi

d

d

x

y

60º

135

ve d

Simedy

an A

kademi

Simedy an A kademi

1

3 tür. Buna göre,

Simedy an A kademi

3

2

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi

3

d

x

B

C(2, m-1)

A

y

O

2

Simedy an A kademi y x A(-2, 5) C(x, 0) B(6, -1) _{en az} 9.

Simedy an A kademi

a) 3x + 2y - 3 = 0

c) y = 4x - 2

b) 2x + y = 0

d) y = 3

2

x - 4

Simedy an A kademi

1

2

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi

3

2

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

Simedy an A kademi y d C 4 3 B A -2 x 19.

Simedy an A kademi

O A

_{B(6, 0)}

C y=

D

y=3x

x

y

Simedy an A kademi A C B y y= 2x x D A(ABCD) kaç br2 21.

Simedy

an A

kademi

y = (2a-4)x + b - 1

Simedy

an A

kademi

Simedy an A kademi

2

3

Buna göre,

Simedy

an A

kademi

Paralel Olan Do rular

d₁ : a₁x + b₁y + c₁ = 0 do rusununun e ...

d₂ : a₂x + b₂y + c₂ = 0 do rusunun e ...

olmak üzere d₁ ve d₂ do rular ... o yönde y klar

r ntlar ...

Paralel do rular rtak noktalar ... y d₁ d₂ x O ... ... m₁ = ... m₂ = ... r r ... ve do rular r r ... d_{1 2} ´ ... = ... ... ...

Simedy an A kademi Örnek-64

(2m+1)x - 3y + 2 = 0

(m+2)x + 2y - 1 = 0

Simedy

an A

kademi

Örnek-65

Simedy an A kademi d₁ : a₁x + b₁y + c₁ ... d₂ : a₂x + b₂y + c₂ ... olmak üzere d₁ ve d₂ ... ... ₁.m₂ = -1) y x d₂ d₁ m₁ = ... m₂ = ... ... = ... ... = ... ... = ... ... = - ... ... ... ... = ... ... . ... = ...

Simedy

an A

kademi

Simedy an A kademi Örnek-66

(k-2)x + 3y - 6 = 0

2x + 4y + 1 = 0

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

Örnek-69

Simedy an A kademi d ₁ : a₁x + b₁y + c₁ = 0 d ₂ : a₂x + b₂y + c₂ = 0 1) ... ... ¹ ... ... ... noktada ... ... ... ... B ... veya ... bulunur. ... A

Simedy an A kademi Örnek-70

3x - y + 9 = 0

x + y - 1 = 0

Simedy an A kademi Örnek-71 x - y + 7 = 0 2x + y - 4 = 0

Simedy an A kademi Örnek-72

y

x

d

d

Simedy an A kademi Örnek-73

y

x

C

B(3,0)

A

y=2x

y=

₃

x

Simedy an A kademi 2) ... ... = ... ... ... ... B ... ... d₁ d₂ ... // ... ... Ç.K = ... olur.

Simedy an A kademi Örnek-74

3x + 2y - 1= 0

(m-1)x + y + 2= 0

Simedy an A kademi 3) ... ... = ... = ..._... ... B ... ... d 1= d2

Simedy an A kademi Örnek-75

(2a-1)x - 3y + 4 = 0

2x + y - b + 1 = 0

Simedy an A kademi A(x₁, y₁) d: ax+by+c=0 x y H ... ... |AH| = ..._... ... y

Simedy

an A

kademi

Örnek-76

Simedy

an A

kademi

Simedy an A kademi Örnek-78 3 6 d y x A(5, 1) A

Simedy

an A

kademi

Simedy an A kademi Paralel k ru Ar k Uzak A r r ralel olan d₁: ax + by + c₁ = 0 d₂: ax + by + c₂ = 0

do rular ver k ru ar k k rhang ru üzer ruy ... Bu uzak h = |_......| r. x y d₁ d₂ a a ... A _. . H ...

Simedy

an A

kademi

Örnek-80

Simedy an A kademi Örnek-81

3x - y + 2 = 0

6x - 2y + 3 = 0

Simedy

an A

kademi

Örnek-82

Simedy an A kademi 1.

(3a-1)x - y + 2 = 0

(a+2)x + 2y - 1 = 0

Simedy

an A

kademi

2.

Simedy an A kademi 3.

(2a-1)x + 2y - 3 = 0

4x - 3y + 1 = 0

Simedy

an A

kademi

Simedy

an A

kademi

Simedy

an A

kademi

6.

Simedy an A kademi 7.

2x - 3y + 7 = 0

x - y - 2 = 0

Simedy an A kademi 8. x + 2y - 1 = 0 x + y + 2 = 0

Simedy an A kademi 9. y x B(4,0) A H y= 4x . y= x 4

Simedy an A kademi 10.

2x + 3y + 3 = 0

(a-3)x + 2y + 1 = 0

Simedy an A kademi 11.

(a+2)x - 4y + 2 = 0

3x - (b+1)y - 3 = 0

Simedy

an A

kademi

12.

Simedy

an A

kademi

Simedy

an A

kademi

14.

Simedy an A kademi 15.

3x - y + 2 = 0

3x - y - 3 = 0

Simedy an A kademi 16.

2x - y + 3 = 0

4x - 2y + 1 = 0

Simedy

an A

kademi

17.

Simedy an A kademi 1.

göre ,

A) 5

B) 4

C) 3

D) 2

E) 1

Test-1

Simedy an A kademi 2. göre, A) (2, -4) B) (4, -2) C) (0, -3) D) (5, -1) E) (2, -3)

Test-1

Simedy an A kademi 3.

A) 15

B) 10

C) 8

D) 6

E) 2

Test-1

Simedy an A kademi 4. x C B(2, 0) A(0, 2) D(8, 10) y O -ge 2 A) 16 B) 18_ñ2 C) 20 D) 20_ñ2 E) 32

Test-1

Simedy an A kademi 5. A) -2 B) -1 C) 0 D) 2 E) 4

Test-1

Simedy an A kademi 6. y x B C D 0 A(6,0) A(ABCD) = 100 br2 A) (14, 6) B) (10, 8) C) (6, 8) D) (8,14) E) (6, 10)

Test-1

Simedy an A kademi 7. D(a, 4) _{C(4, b-1)} B(2, 3) A(-1, 2)

Buna göre, a.b

A) -4 B) -1 C) 2 D) 4 E) 6

Simedy an A kademi 8. D C(4, -2) A(-1, 5) B(3, 7) Buna göre, A) 3ñ2 B) 4ñ3 C) 5ñ2 D) ò65 E) ò73

Test-1

Simedy an A kademi 9. A) 2ñ2 B) 3 C) 3ñ3 D) ò13 E) 5ñ2

Test-1

Simedy an A kademi 10. A) (6, 3) B) (7, 9) C) (11, 3) D) (5, -2) E) (3, 2)

Test-1

Simedy an A kademi 11. A(-1, 5) (9, -5) A) -2 B) 0 C) 4 D) 5 E) 6

C(x, y)

Test-1

Simedy an A kademi 12. x y _{C(4, 7)} B(-3, b) K 0 D(5, -2) A(a, -3) |AK| = |CK| ve |BK| = |DK| A) -12 B) -10 C) -1 D) 3 E) 7

Test-1