Question

Determine a distância entre dois pontos: a)(-2,-1) (3,-4)

b) (-4,3) (-4,(-7)

c) (1,3) (-3,3)

d) (-1,4) (-2,-3)

e) (5,2) (1,3)

f) (-1,5) (-1, 12)​

Answer 1

$D^{2} = \sqrt{(-4)^{2}+(1)^{2} }$Resposta:

A) $\sqrt{34}$

B) 10

C) 4

D) 2$\sqrt{5}$

E) $\sqrt{17$

F) 7

Explicação passo a passo:

a)(-2,-1) (3,-4)

$D^{2} = \sqrt{(xB-xA)^{2}+(yB-yA)^{2}$

$D^{2} = \sqrt{(3-(-2))^{2}+(-4-(-1))^{2} }$

$D^{2} = \sqrt{(3+2)^{2}+(-4+1)^{2}}$

$D^{2} = \sqrt{(5)^{2}+(-3)^{2}$

$}\sqrt{D}= \sqrt{(25+9)}$

$D=\sqrt{34}$

b) (-4,3) (-4,(-7)

$D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}$

$D^{2} = \sqrt{(-4-(-4))^{2}+(-7-3)^{2} }$

$D^{2} = \sqrt{(-4+4)^{2}+(-7-3)^{2} }$

$D^{2} = \sqrt{(0)+(-10)^{2} }$

$\sqrt{D} = \sqrt{100}$

D=10

c) (1,3) (-3,3)

$D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}$

$D^{2} = \sqrt{(-3-1)^{2}+(3-3)^{2} }$

$D^{2} = \sqrt{(-4)^{2}+(0)^{2} }$

$\sqrt{D} = \sqrt{(16) }$
D=4

d) (-1,4) (-2,-3)

$D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}$

$D^{2} = \sqrt{(2-(-1))^{2}+(-3-4)^{2} }$

$D^{2} = \sqrt{(2+1)^{2}+(-3-4)^{2} }$

$D^{2} = \sqrt{(-1)^{2}+(-7)^{2} }$

$D^{2} = \sqrt{(1+49)} }$
$\sqrt{D}= \sqrt{(50)} }$
D= 2$\sqrt{5}$

e) (5,2) (1,3)

$D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}$

$D^{2} = \sqrt{(1-5)^{2}+(3-2)^{2} }$

$D^{2} = \sqrt{(-4)^{2}+(1)^{2} }$

$D^{2} = \sqrt{(16+1}$

$\sqrt{D} = \sqrt{17}$

D= $\sqrt{17}$

f) (-1,5) (-1, 12)​

$D^{2}= \sqrt{(xB-xA)^{2}+(yB-yA)^{2}}$

$D^{2} = \sqrt{(-1-(-1))^{2}+(12-5)^{2} }$

$D^{2} = \sqrt{(-1+1))^{2}+(12-5)^{2} }$

$D^{2} = \sqrt{(0))^{2}+(7)^{2} }$

$\sqrt{D}=\sqrt{21}$

D=7