a) marvin walks a straight line from (-5,2) to (3,1) (-3,1) to (-1 -4). what is the approximate distance marvin travels?

Question

Accepted Answer

# Explanation:
## Step1: Calculate the distance between $(-5,2)$ and $(3,1)$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-5,y_1 = 2,x_2=3,y_2=1$.
$$
\begin{align*}
d_1&=\sqrt{(3-(-5))^2+(1 - 2)^2}\
&=\sqrt{(3 + 5)^2+(-1)^2}\
&=\sqrt{8^2+1}\
&=\sqrt{64 + 1}\
&=\sqrt{65}\approx 8.06
\end{align*}
$$
## Step2: Calculate the distance between $(-3,1)$ and $(-1,-4)$
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-3,y_1 = 1,x_2=-1,y_2=-4$.
$$
\begin{align*}
d_2&=\sqrt{(-1-(-3))^2+(-4 - 1)^2}\
&=\sqrt{(-1 + 3)^2+(-5)^2}\
&=\sqrt{2^2+25}\
&=\sqrt{4+25}\
&=\sqrt{29}\approx5.39
\end{align*}
$$
## Step3: Calculate the total distance
The total distance $D=d_1 + d_2$.
$$D\approx8.06+5.39 = 13.45$$

# Answer:
$13.45$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the distance between \((-5,2)\) and \((3,1)\)

Step2: Calculate the distance between \((-3,1)\) and \((-1,-4)\)

Step3: Calculate the total distance

Answer: