find the distance, d, of $ \overline { a b } $.
$ a = ( - 5,1 ) \quad b = ( 1, - 3 ) $
$ d = $
$ d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } $
round to the nearest tenth

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Accepted Answer

# Explanation:
## Step1: Identify coordinates
Let $A(-5,1)$ be $(x_1,y_1)$ and $B(1,-3)$ be $(x_2,y_2)$.
## Step2: Substitute into distance formula
$$
\begin{align*}
d&=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\
&=\sqrt{(1-(-5))^2+(-3 - 1)^2}\
&=\sqrt{(1 + 5)^2+(-4)^2}\
&=\sqrt{6^2+(-4)^2}\
&=\sqrt{36 + 16}\
&=\sqrt{52}\
&\approx7.2
\end{align*}
$$

# Answer:
$7.2$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify coordinates

Step2: Substitute into distance formula

Answer: