calculate the distance between the points ( k=(5,0) ) and ( p=(1,-7) ) in the coordinate plane. give an exact answer (not a decimal approximation).

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
The coordinates of point $K=(5,0)$ and $P=(1, - 7)$.
## Step2: Use the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Substitute $x_1 = 5,y_1=0,x_2 = 1,y_2=-7$ into the formula:
$$
\begin{align*}
d&=\sqrt{(1 - 5)^2+(-7 - 0)^2}\
&=\sqrt{(-4)^2+(-7)^2}\
&=\sqrt{16 + 49}\
&=\sqrt{65}
\end{align*}
$$

# Answer:
$\sqrt{65}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

Step2: Use the distance formula

Answer: