Question

a truck begins its weekly route at the recycling plant at point a, as pictured on the coordinate - plane below. it travels from point a to point d, then to points c, b, and e, respectively, before returning to the recycling plant at point a at the end of the day. the trucks route is described on the coordinate plane. if each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route to the nearest hundredth?

13.30 miles
19 miles
22.62 miles
30 miles

Explanation:

Explicación:

Paso 1: Encontrar la distancia entre puntos

Utilizamos la fórmula de distancia $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Paso 2: Distancia entre A(-2, 5) y B(2, 5)

$d_{AB}=\sqrt{(2 - (-2))^2+(5 - 5)^2}=\sqrt{(4)^2+0^2}=4$

Paso 3: Distancia entre B(2, 5) y C(4, 1)

$d_{BC}=\sqrt{(4 - 2)^2+(1 - 5)^2}=\sqrt{(2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Paso 4: Distancia entre C(4, 1) y D(2, - 3)

$d_{CD}=\sqrt{(2 - 4)^2+(-3 - 1)^2}=\sqrt{(-2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Paso 5: Distancia entre D(2, -3) y A(-2, 5)

$d_{DA}=\sqrt{(-2 - 2)^2+(5 - (-3))^2}=\sqrt{(-4)^2+(8)^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\approx8.94$

Paso 6: Sumar distancias

$d_{total}=d_{AB}+d_{BC}+d_{CD}+d_{DA}=4 + 4.47+4.47+8.94 = 22.88\approx22.82$

Respuesta:

22.82 millas

Answer:

Explicación:

Paso 1: Encontrar la distancia entre puntos

Utilizamos la fórmula de distancia $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Paso 2: Distancia entre A(-2, 5) y B(2, 5)

$d_{AB}=\sqrt{(2 - (-2))^2+(5 - 5)^2}=\sqrt{(4)^2+0^2}=4$

Paso 3: Distancia entre B(2, 5) y C(4, 1)

$d_{BC}=\sqrt{(4 - 2)^2+(1 - 5)^2}=\sqrt{(2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Paso 4: Distancia entre C(4, 1) y D(2, - 3)

$d_{CD}=\sqrt{(2 - 4)^2+(-3 - 1)^2}=\sqrt{(-2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$

Paso 5: Distancia entre D(2, -3) y A(-2, 5)

$d_{DA}=\sqrt{(-2 - 2)^2+(5 - (-3))^2}=\sqrt{(-4)^2+(8)^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\approx8.94$

Paso 6: Sumar distancias

$d_{total}=d_{AB}+d_{BC}+d_{CD}+d_{DA}=4 + 4.47+4.47+8.94 = 22.88\approx22.82$

Respuesta:

22.82 millas