Question

Calcule a distância entre os seguintes pontos (se vier com palhaçada já sabe né)
L(2,-1) e P(2,-6)
M(6,3) e Q(-4,-5)
C(0,-8) e A(5,5)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{d_{PL} = \sqrt{(x_P - x_L)^2 + (y_P - y_L)^2}}$

$\mathsf{d_{PL} = \sqrt{(2 - 2)^2 + (-6 - (-1))^2}}$

$\mathsf{d_{PL} = \sqrt{(2 - 2)^2 + (-6 + 1)^2}}$

$\mathsf{d_{PL} = \sqrt{(0)^2 + (-5)^2}}$

$\mathsf{d_{PL} = \sqrt{0 + 25}}$

$\mathsf{d_{PL} = \sqrt{25}}$

$\boxed{\boxed{\mathsf{d_{PL} = 5}}}$

$\mathsf{d_{QM} = \sqrt{(x_Q - x_M)^2 + (y_Q - y_M)^2}}$

$\mathsf{d_{QM} = \sqrt{(-4 -6)^2 + (-5 - 3)^2}}$

$\mathsf{d_{QM} = \sqrt{(-4 + 6)^2 + (-5 - 3)^2}}$

$\mathsf{d_{QM} = \sqrt{(10)^2 + (-8)^2}}$

$\mathsf{d_{QM} = \sqrt{100 + 64}}$

$\mathsf{d_{QM} = \sqrt{164}}$

$\boxed{\boxed{\mathsf{d_{QM} = 2\sqrt{41}}}}$

$\mathsf{d_{AC} = \sqrt{(x_A - x_C)^2 + (y_A - y_C)^2}}$

$\mathsf{d_{AC} = \sqrt{(5 - 0)^2 + (5 - (-8))^2}}$

$\mathsf{d_{AC} = \sqrt{(5 - 0)^2 + (5 + 8)^2}}$

$\mathsf{d_{AC} = \sqrt{(5)^2 + (13)^2}}$

$\mathsf{d_{AC} = \sqrt{25 + 169}}$

$\boxed{\boxed{\mathsf{d_{AC} = \sqrt{194}}}}$

Answer 2

Resposta:

d²=(x1-x2)²+(y1-y2)²

a)

L(2,-1) e P(2,-6)

d²=(2-2)²+(-1+6)²

d²=0²+5²

d=5  unid. de distância

b)

M(6,3) e Q(-4,-5)

d²=(6+4)²+(3+5)²

d²=10²+8²

d²=100+64

d=2√41 unid. de distância

c)

C(0,-8) e A(5,5)

d²=(0-5)²+(-8-5)²

d²=5²+13²

d²=25+169

d²= √194  unid. de distância