find the distance between the pair of points $(-4,-7)$ and $(2,-6)$. if necessary, express the answer in simplified radical form and then round to two decimal places. the distance between the given points is $square$ units. (simplify your answer. type an exact answer, using radicals as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
Let $(x_1,y_1)=(-4,-7)$ and $(x_2,y_2)=(2,-6)$
## Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
Substitute the values:
$$
\begin{align*}
d&=\sqrt{(2-(-4))^2+(-6 - (-7))^2}\
&=\sqrt{(2 + 4)^2+(-6+7)^2}\
\end{align*}
$$
## Step3: Simplify the expressions inside the square root
$$
\begin{align*}
d&=\sqrt{6^2+1^2}\
&=\sqrt{36 + 1}\
&=\sqrt{37}
\end{align*}
$$

# Answer:
$\sqrt{37}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Step3: Simplify the expressions inside the square root

Answer: