distance formula
find ab given a(-4,6) and b(3,-1)
*simplify the radical
find ef given e(-7,-2) and f(11,3)
*round to the nearest tenths

Question

Accepted Answer

# Explanation:
## Step1: Recall 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: Calculate AB
For points $A(-4,6)$ and $B(3,-1)$, $x_1=-4,y_1 = 6,x_2=3,y_2=-1$.
$$
\begin{align*}
AB&=\sqrt{(3-(-4))^2+((-1)-6)^2}\
&=\sqrt{(3 + 4)^2+(-7)^2}\
&=\sqrt{7^2+(-7)^2}\
&=\sqrt{49 + 49}\
&=\sqrt{98}\
&=\sqrt{49\times2}\
&=7\sqrt{2}
\end{align*}
$$
## Step3: Calculate EF
For points $E(-7,-2)$ and $F(11,3)$, $x_1=-7,y_1=-2,x_2 = 11,y_2=3$.
$$
\begin{align*}
EF&=\sqrt{(11-(-7))^2+(3-(-2))^2}\
&=\sqrt{(11 + 7)^2+(3 + 2)^2}\
&=\sqrt{18^2+5^2}\
&=\sqrt{324+25}\
&=\sqrt{349}\
&\approx18.7
\end{align*}
$$
# Answer:
AB = $7\sqrt{2}$, EF $\approx18.7$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall distance formula

Step2: Calculate AB

Step3: Calculate EF

Answer: