Question

calculate the distance between the points e = (-8, 9) and p = (-1, 1) in the coordinate plane. give an exact answer (not a decimal approximation).

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: Identify coordinates

For points \(E = (-8,9)\) and \(P = (-1,1)\), we have \(x_1=-8,y_1 = 9,x_2=-1,y_2 = 1\).

Step3: Substitute into formula

Substitute the values into the formula:
\[

$$\begin{align*} d&=\sqrt{(-1 - (-8))^2+(1 - 9)^2}\\ &=\sqrt{(-1 + 8)^2+(-8)^2}\\ &=\sqrt{(7)^2+(-8)^2}\\ &=\sqrt{49 + 64}\\ &=\sqrt{113} \end{align*}$$

\]

Answer:

$\sqrt{113}$