find the distance, d, of $ \overline { a b } $.
$ a = ( 2,1 ) \quad b = ( - 4,7 ) $
$ d = $
$ d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } $
round to the nearest tenth

Question

Accepted Answer

# Explanation:
## Step1: Identify coordinates
Let $A=(x_1,y_1)=(2,1)$ and $B=(x_2,y_2)=(-4,7)$
## Step2: Substitute into distance formula
$$
\begin{align*}
d&=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\
&=\sqrt{(-4 - 2)^2+(7 - 1)^2}\
&=\sqrt{(-6)^2+6^2}\
&=\sqrt{36 + 36}\
&=\sqrt{72}\
&=6\sqrt{2}\
&\approx8.5
\end{align*}
$$

# Answer:
$8.5$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify coordinates

Step2: Substitute into distance formula

Answer: