Question

5) Determine a distância do ponto C(2;3):

a) Ao ponto F (0; - 3);

b) À origem do plano cartesiano;

c) Ao eixo das ordenadas.

me ajudem pfv ;-;
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Answer 1

Resposta:

Sendo a fórmula \begin{gathered}D=\sqrt{(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}}\\\end{gathered}

D=

(x

b

−x

a

)

2

+(y

b

−y

a

)

2

a)

\begin{gathered}D=\sqrt{(0-2)^{2}+(-3-3)^{2}}\\D=\sqrt{(-2)^{2}+(-6)^{2}}\\D=\sqrt{4+36}\\D=\sqrt{40}\\\end{gathered}

D=

(0−2)

2

+(−3−3)

2

D=

(−2)

2

+(−6)

2

D=

4+36

D=

40

Decompondo fica: 2\sqrt{10}2

10

b)

\begin{gathered}D=\sqrt{(0-2)^{2}+(0-3)^{2}}\\D=\sqrt{(-2)^{2}+(-3)^{2}}\\D=\sqrt{4+9}\\D=\sqrt{13}\\\end{gathered}

D=

(0−2)

2

+(0−3)

2

D=

(−2)

2

+(−3)

2

D=

4+9

D=

13

c)

\begin{gathered}D=\sqrt{(0-2)^{2}+(3-3)^{2}}\\D=\sqrt{(-2)^{2}+0}\\D=\sqrt{4}\\D=2\end{gathered}

D=

(0−2)

2

+(3−3)

2

D=

(−2)

2

+0

D=

4

D=2