Question

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

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 $\approx18.7$