graph the points and find the distance between each set of points. when necessary, round to the nearest tenth.
6. $(0,-3)$ and $(3,4)$
7. $(-2,1)$ and $(6,-5)$

Question

Accepted Answer

# Explanation:
## Step1: Identify the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

## Step2: Solve for problem 6
For the points $(0,-3)$ and $(3,4)$, $x_1 = 0,y_1=-3,x_2 = 3,y_2 = 4$
$$
\begin{align*}
d&=\sqrt{(3 - 0)^2+(4-(-3))^2}\
&=\sqrt{3^2 + 7^2}\
&=\sqrt{9+49}\
&=\sqrt{58}\
&\approx7.6
\end{align*}
$$

## Step3: Solve for problem 7
For the points $(-2,1)$ and $(6,-5)$, $x_1=-2,y_1 = 1,x_2=6,y_2=-5$
$$
\begin{align*}
d&=\sqrt{(6-(-2))^2+(-5 - 1)^2}\
&=\sqrt{8^2+(-6)^2}\
&=\sqrt{64 + 36}\
&=\sqrt{100}\
&=10
\end{align*}
$$

# Answer:
6. The distance is approximately $7.6$
7. The distance is $10$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the distance formula

Step2: Solve for problem 6

Step3: Solve for problem 7

Answer: