Question

Zadania w załączniku.

Answer 1

z.1

A = ( - 5; - 1) ,  B = ( 1; - 3),  C = ( 3; 3 )

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z.2

A = ( - 4; - 2),  B = ( 2; 1) ,  C = ( 0; 3)  , D = ( - 2; 2)

 

Prosta AB

y = a x + b

czyli

- 2 = - 4a + b

1 = 2a + b

-------------------       odejmujemy stronami

- 2 - 1 =  - 4a  - 2a

- 3 = - 6a  / : ( - 6)

a = 1/2 = 0,5

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lub

a = [ 1 - (-2)] /[ 2 - (-2)] = 3/6 = 1/2 = 0,5

===============================

Prosta  BC

 a1 = [ 3 - 1]/ [ 0 - 2] = 2 / (-2) = - 1

=========================

Prosta  CD

a2 = [ 2 - 3] /[ - 2 - 0 ] = (-1) / (-2) = 1/2 = 0,5

================================

Prosta AD

a3 = [  2 - (-2)] / [ - 2 - (-4)] = 4 / 2 = 2

===========================

 Wzór:

A = ( x1; y1)  ,  B = ( x2; y2)

to

a = ( y2 - y1 ) / ( x2 - x1)

===================

z.3

 

a)   P = ( 3; 4),  Q= ( 7; 6)

 y = a x + b

więc

4 = 3a + b

6 = 7a + b

----------------  odejmujemy stronami

6 - 4 = 7a - 3a

2 = 4a  / : 4

a = 2/4 = 1/2= 0,5

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b = 4 - 3a = 4 - 3*0,5 = 4 - 1,5 = 2,5

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Odp.   y =  0,5 x + 2,5

=================

b)

P = ( - 2; 7), Q = ( 2; - 1)

więc

7 = -2a + b

- 1 = 2a + b

-----------------  odejmujemy stronami

7 - (-1) =  -2a - 2a

8 = - 4a  / : ( -4)

- 2 = a

a = - 2

---------

b = - 1 - 2a = - 1 - 2*(-2) = - 1 + 4 = 3

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Odp.   y = -2 x + 3

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c)

P = ( 1/3 ; 1 ) ,  Q = ( 1/2 ;  - 1)

 

więc

1 = (1/3) a + b

- 1 = (1/2) a + b

-----------------------  odejmujemy stronami

1 - (-1) = (1/3) a  - (1/2) a

2 = (2/6) a - (3/6) a

2 = - (1/6) a    / *( -6)

a = - 12

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b = 1 - (1/3) a = 1 - (1/3)*( - 12) = 1 + 4 = 5

---------------------------------------------------------

Odp.  y = - 12 x + 5

====================

d)

P = ( 3; 7/3)   ,  Q = ( 2;  1/3 )

 

Mamy

7/3 = 3a + b

1/3 = 2a + b

-----------------  odejmujemy stronami

7/3 - 1/3 = a

a = 6/3 = 2

-----------------

b = 7/3 - 3a = 7/3 - 3*2 = 7/3 - 6 = 7/3 - 18/3 = - 11/3

-----------------------------------------------------------------------

Odp.  y = 2 x -  11/3

================

e)

P = ( -2; - 6)  ,  Q = ( 8; - 6)

Mamy

- 6  = -2a + b

- 6 = 8a + b

--------------------  odejmujemy stronami

- 6 - (-6) = -2a - 8a

0 = - 10 a

a =  0

----------

b = - 6 + 2a = - 6 + 0 = - 6

-----------------------------------

Odp.   y =  - 6

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Pozostałe przyklady rozwiązujemy w ten sam sposób.