Question

c) Calcule a distância entre os pontos P(-2,3) e Q(-5,-9)
d) Encontre a distância entre os pontos dados: a) L(-4, 3) e M(-4, -7) b) Q(1, 3) e R(-3, 3)

Answer 1

c) Temos que:

$\overline{PQ}=\sqrt{(-2+5)^2+(3+9)^2}$

$\overline{PQ}=\sqrt{3^2+12^2}$

$\overline{PQ}=\sqrt{9+144}$

$\overline{PQ}=\sqrt{153}$

$\overline{PQ}=3\sqrt{17}$

d)

a) $\overline{LM}=\sqrt{(-4+4)^2+(3+7)^2}$

$\overline{LM}=\sqrt{0^2+10^2}$

$\overline{LM}=\sqrt{0+100}$

$\overline{LM}=\sqrt{100}$

$\overline{LM}=10$

b) $\overline{QR}=\sqrt{(1+3)^2+(3-3)^2}$

$\overline{QR}=\sqrt{4^2+0^2}$

$\overline{QR}=\sqrt{16+0}$

$\overline{QR}=\sqrt{16}$

$\overline{QR}=4$

Answer 2

Explicação passo-a-passo:

olá,

P(-2,3) >>> (x1, y1)

Q(-5,-9) >> (x2, y2)

d = √(x2 - x1)² + (y2 - y1)²

d = √(-5 + 2)² + (-9 - 3)²

d = √(-3)² + (-12)²

d = √9 + 144

d = √153

d = √3²•17

d = 3√17

——————

L(-4, 3) >>> (x1, y1)

M(-4, -7) >> (x2, y2)

d = √(x2 - x1)² + (y2 - y1)²

d = √(-4 + 4)² + (-7 - 3)²

d = √(0)² + (-10)²

d = √0 + 100

d = √100

d = √10²

d = 10

—————

Q(1, 3) >>> (x1, y1)

R(-3, 3) >> (x2, y2)

d = √(x2 - x1)² + (y2 - y1)²

d = √(-3 - 1)² + (3 - 3)²

d = √(-4)² + (0)²

d = √16 + 0

d = √16

d = √4²

d = 4

——————

bons estudos!