Question

1.17 zalres roz z matmy klasa 2 na teraz potrzebne

Answer 1

Odpowiedź:

A(- 2, - 3)   B( 1, 4)    C ( - 1, 3)

a)

I AB I² = ( 1 - (-2))² + (4 - (-3))² = 3² + 7² = 9 + 49 = 58

I AB I  = [tex]\sqrt{58}[/tex]

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I BC I² = ( - 1 - 1 )² + ( 3 - 4)² = ( - 2)² + ( - 1)² = 4 + 1 = 5

I BC I = [tex]\sqrt{5}[/tex]

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I AC I² = ( - 1 - ( -2))² + ( 3 - ( - 3))² = 1² + 6² = 1 + 36 = 37

I AC I = [tex]\sqrt{37}[/tex]

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Obwód Δ ABC

L = [tex]\sqrt{58} + \sqrt{5} + \sqrt{37}[/tex]

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b )

D - środek  AC

D ( [tex]\frac{- 1 - 2}{2} , \frac{- 3 +3}{2}[/tex] )            D ( - [tex]\frac{3}{2} , 0 )[/tex]

B ( 1, 4 )

więc

I BD I² = ( [tex]\frac{3}{2} - 1 )^2 + ( 0 - 4)^2 = ( - \frac{5}{2})^2 + ( - 4)^2 = \frac{25}{4} + 16 = \frac{25}{4} + \frac{64}{4} = \frac{89}{4}[/tex]

I BD I  =  [tex]\sqrt{\frac{89}{4} } = \frac{\sqrt{89} }{\sqrt{4} } = \frac{\sqrt{89} }{2}[/tex]

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