Question

Calcule a distância entre a e b em cada caso

a) A(2,5) e B(-5,-2)
B) A (12,2) e B (4,8)
C) A (1, 4) e B (-6,3)
D) A (-2,8) e B (2,9)
E) A (2, 1) e B (4,-1)
F) A (1, 2) e B (0, 1)
G) A (4,-5) e B (-1, 7)
H) A (5,3) e B (2, 7)
I) A (1, 4) e B (-1, 1)
J) A (-2,3) e B (0, 5)

Me ajudem

Answer 1

Explicação passo-a-passo:

a) A(2,5) e B(-5,-2)

A(2,5)

xa=2

ya=5

B(-5,-2)

xb=-5

yb=-2

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

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

$d = \sqrt{7 {}^{2} + 7 {}^{2} }$

$d = \sqrt{49 + 49}$

$d = \sqrt{98}$

$d = \sqrt{7 {}^{2} \times 2}$

$d = \sqrt{7 {}^{2} } \sqrt{2}$

d=7√2

B) A (12,2) e B (4,8)

A(12,2)

xa=12

ya=2

B(4,8)

xb=4

yb=8

$d = \sqrt{(12 - 4) {}^{2} + (2 - 8) {}^{2} }$

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

$d = \sqrt{64 + 36}$

$d = \sqrt{100}$

d=10

C) A (1, 4) e B (-6,3)

A(1,4)

xa=1

ya=4

B(-6,3)

xb=-6

yb=3

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

$d = \sqrt{(1 - ( - 6)) {}^{2} + (4 - 3) {}^{2} }$

$d = \sqrt{(1 + 6) {}^{2} + (4 - 3) {}^{2} }$

$d = \sqrt{7 {}^{2} + 1 {}^{2} }$

$d = \sqrt{49 + 1}$

$d = \sqrt{50}$

$d = \sqrt{5 {}^{2} \times 2}$

$d = \sqrt{5 {}^{2} } \sqrt{2}$

d=5√2

D) A (-2,8) e B (2,9)

A(-2,8)

xa=-2

ya=8

B(2,9)

xb=2

yb=9

$d = \sqrt{( - 2 - 2) {}^{2} + (8 - 9) {}^{2} }$

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

$d = \sqrt{16 + 1}$

d=√17

E) A (2, 1) e B (4,-1)

A(2,1)

xa=2

ya=1

B(4,-1)

xb=4

yb=-1

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

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

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

$d = \sqrt{4 + 4}$

$d = 8 \sqrt{2}$

$d = \sqrt{ {2}^{2} \times 2 }$

$d = \sqrt{2 {}^{2} } \sqrt{2}$

d=2√2

F) A (1, 2) e B (0, 1)

A(1,2)

xa=1

ya=2

B(0,1)

xb=0

yb=1

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

$d = \sqrt{1 {}^{2} + 1 {}^{2} }$

$d = \sqrt{1 + 1}$

d=√2

G) A (4,-5) e B (-1, 7)

A(4,-5)

xa=4

ya=-5

B(-1,7)

xb=-1

yb=7

$d = \sqrt{(4 - ( - 1)) {}^{2} + ( - 5 - 7) {}^{2} }$

$d = \sqrt{(4 + 1) {}^{2} + ( - 5 - 7) {}^{2} }$

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

$d = \sqrt{25 + 144}$

$d = \sqrt{169}$

d=13

H) A (5,3) e B (2, 7)

A(5,3)

xa=5

ya=3

B(2,7)

xb=2

yb=7

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

$d = \sqrt{(5 - 2) {}^{2} + (3 - 7) {}^{2} }$

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

$d = \sqrt{9 + 16}$

$d = \sqrt{25}$

d=5

I) A (1, 4) e B (-1, 1)

A(1,4)

xa=1

ya=4

B(-1,1)

xb=-1

yb=1

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

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

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

$d = \sqrt{2 {}^{2} + 3 {}^{2} }$

$d = \sqrt{4 + 9}$

d=√13

J) A (-2,3) e B (0, 5)

A(-2,3)

xa=-2

ya=3

B(0,5)

xb=0

yb=5

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

$d = \sqrt{( - 2 - 0) {}^{2} + (3 - 5) {}^{2} }$

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

$d = \sqrt{4 + 4}$

$d = \sqrt{8}$

$d = \sqrt{2 {}^{2} \times 2 }$

$d = \sqrt{2 {}^{2} } \sqrt{2}$

d=2√2