Question

Determine a distância entre os pontos dados.

a) A(5, 2) e B(1, 3)

b) C(21, 4) e D(22, 23)

c) E(24, 23) e O(0, 0)

d) F(25, 4) e G(2, 25)

e) H(21, 5) e I(21, 12)

f) J(22, 21) e K(3, 24)

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Answer 1

Resposta:

A) d(a,b)= √(x₂-x₁)²+(y₂-y₁)²

d(a,b)= √(5-1)²+(3-2)²

d(a,b)= √4²+1²

d(a,b)= √16+1= √17

B) d(e,o)=√(x₂-x₁)²+(y₂-y₁)²

d(e,o)= √(0+4)²+(0+3)²

d(e,o)= √4²+3²

d(e,o)= √16+9

d(e,o)= √25= 5

C) d(f,g)= √(x₂-x₁)²+(y₂-y₁)²

d(f,g)= √(2+5)²+(4+5)²

d(f,g)= √7²+9²

d(f,g)= √49+81

d(f,g)= √130

D) d(h,i)= √(x₂-x₁)²+(y₂-y₁)²

d(h,i)= √(-1+1)²+(12-5)²

d(h,i)= √0²+7²

d(h,i)= √49= 7

E) d(j,i)= √(x₂-x₁)²+(y₂-y₁)²

d(j,i)= √(3+2)²+(-1+4)²

d(j,i)= √5²+3²

d(j,i)= √25+9

d(j,i)= √34

F) d(l,m)= √(x₂-x₁)²+(y₂-y₁)²

d(l,m)= √(-4+4)²+(3+7)²

d(l,m)= √0²+10²

d(l,m)= √100= 10

G) d(n,p)= √(x₂-x₁)²+(y₂-y₁)²

d(n,p)= √(√2+√2)²+(√2+√2)²

d(n,p)= √(2+2+2+2)+(2+2+2+2)

d(n,p)= √8+8

d(n,p)= √16= 4

H) d(q,r)= √(x₂-x₁)²+(y₂-y₁)²

d(q,r)= √(1+3)²+(3-3)²

d(q,r)= √4²+0²

d(q,r)= √16= 4

Explicação passo-a-passo:

Answer 2

Resposta:

a) A(5, 2) e B(1, 3)  

(a,b)= √(x₂-x₁)²+(y₂-y₁)²

(a,b)= √(5-1)²+(3-2)²

(a,b)= √4²+1²

(a,b)= √16+1= √17

b) C(21, 4) e D(22, 23)  

(c,d)=√(x₂-x₁)²+(y₂-y₁)²

= √(21-22)²+(4+23)²

= √1²+19²

= √1+361

= √362= 19

c) E(24, 23) e O(0, 0)  

(e,o)= √(x₂-x₁)²+(y₂-y₁)²

= √(24-0)²+(23-0)²

= √24²+23²

= √576+529

= √1105=33,24

d) F(25, 4) e G(2, 25)  

(f,g)= √(x₂-x₁)²+(y₂-y₁)²

= √(25-2)²+(4-25)²

= √23²+19²  

=529+361

= √890= 29,83

e) H(21, 5) e I(21, 12)  

(h,i)= √(x₂-x₁)²+(y₂-y₁)²

= √(21-21)²+(5-12)²

= √0²+7²

= √19=7

f) J(22, 21) e K(3, 24)

(j,k)= √(x₂-x₁)²+(y₂-y₁)²

= √(22-3)²+(21-24)²

= √19²+3²

= √361+9

= √370= 19,23

Explicação passo-a-passo: