calculate the distance between the points ( f = (-4, -2) ) and ( h = (1, 3) ) in the coordinate plane. give an exact answer (not a decimal approximation).

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
Let $F(-4,-2)$ be $(x_1,y_1)$ and $H(1,3)$ be $(x_2,y_2)$.
## Step2: Use the distance formula
The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Substitute $x_1=-4,y_1 = - 2,x_2=1,y_2 = 3$ into the formula:
$$
\begin{align*}
d&=\sqrt{(1-(-4))^2+(3 - (-2))^2}\
&=\sqrt{(1 + 4)^2+(3+2)^2}\
&=\sqrt{5^2+5^2}\
&=\sqrt{25 + 25}\
&=\sqrt{50}\
&=\sqrt{25\times2}\
&=5\sqrt{2}
\end{align*}
$$

# Answer:
$5\sqrt{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

Step2: Use the distance formula

Answer: