Question

find the distance between the pair of points.
e(4, -4), f(-2,4)

d = \\(\square\\) (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

For points \( E(4, -4) \) and \( F(-2, 4) \), we have \( x_1 = 4 \), \( y_1 = -4 \), \( x_2 = -2 \), \( y_2 = 4 \).

Step3: Substitute into formula

Substitute the values into the distance formula:
\[

$$\begin{align*} d&=\sqrt{(-2 - 4)^2 + (4 - (-4))^2}\\ &=\sqrt{(-6)^2 + (8)^2}\\ &=\sqrt{36 + 64}\\ &=\sqrt{100} \end{align*}$$

\]

Step4: Simplify the radical

\( \sqrt{100} = 10 \).

Answer:

\( 10 \)