Question

3) Calcule a distância entre os pontos: a) A(1:2) e B( 4; 6) b) A(-3:5) e B(3:13) c) A(-1; 3) e B(-1;-1) d) A(0:3) e B(3; -7) e) A(0:0) e B(1,1) 1) A(1:3) e B(9:9) g) A(-3; 1) e B( 5:-14) h) A(-12:9) e B(0:0)​

Answer 1

Explicação passo-a-passo:

Resolução!!!

a) A(1:2) e B( 4; 6)

A(1:2)

xa=1

ya=2

B( 4; 6)

xb=4

yb=6

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{(1 - 4) {}^{2} + (2 - 6) {}^{2} }$

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

$d = \sqrt{9 + 16}$

$d = \sqrt{25}$

d=5

______________________

b) A(-3:5) e B(3:13)

A(-3:5)

xa=-3

ya=5

B(3:13)

xb=3

yb=13

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{( - 3 - 3) {}^{2} + (5 - 13) {}^{2} }$

$d = \sqrt{( - 6) {}^{2} + ( - 8) {}^{2} }$

$d = \sqrt{36 + 64}$

$d = \sqrt{100}$

d=10

______________________

c) A(-1; 3) e B(-1;-1)

A(-1; 3)

xa=-1

ya=3

B(-1;-1)

xb=-1

yb=-1

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

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

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

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

$d = \sqrt{0 + 16}$

$d = \sqrt{16}$

d=4

______________________

d) A(0:3) e B(3; -7)

A(0:3)

xa=0

ya=3

B(3; -7)

xb=3

yb=-7

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{(0 - 3) {}^{2} + (3 - ( - 7) {}^{2} }$

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

$d = \sqrt{9 + (10) {}^{2} }$

$d = \sqrt{9 + 100}$

d=√109

______________________

e) A(0:0) e B(1,1)

A(0:0)

xa=0

ya=0

B(1,1)

xb=1

yb=1

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{(0 - 1) {}^{2} + (0 - 1) {}^{2} }$

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

$d = \sqrt{1 + 1}$

d=√2

______________________

f) A(1:3) e B(9:9)

A(1:3)

xa=1

ya=3

B(9:9)

xb=9

yb=9

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{(1 - 9) {}^{2} + (3 - 9) {}^{2} }$

$d = \sqrt{( - 8) {}^{2} + ( - 6) {}^{2} }$

$d = \sqrt{64 + 36}$

$d = \sqrt{100}$

d=10

______________________

g) A(-3; 1) e B( 5:-14)

A(-3; 1)

xa=-3

ya=1

B( 5:-14)

xb=5

yb=-14

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{( - 3 - 5) {}^{2} + ( 1 - ( - 14) {}^{2} }$

$d = \sqrt{( - 8) {}^{2} + (1 + 14) {}^{2} }$

$d = \sqrt{64 + (15) {}^{2} }$

$d = \sqrt{64 + 225}$

$d = \sqrt{289}$

d=17

______________________

h) A(-12:9) e B(0:0)

A(-12:9)

xa=-12

ya=9

B(0:0)

xb=0

yb=0

$d = \sqrt{(xa - xb) {}^{2} + (ya - yb) {}^{2} }$

$d = \sqrt{( - 12 - 0) {}^{2} + (9 - 0) {}^{2} }$

$d = \sqrt{( - 12) {}^{2} + (9) {}^{2} }$

$d = \sqrt{144 + 81}$

$d = \sqrt{225}$

d=15

Espero ter ajudado!