Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates of the two points

Let the two points be \( (x_1,y_1)=(4,-8) \) and \( (x_2,y_2)=(8,-4) \)

Step2: Use the distance formula \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \)

Substitute \( x_1 = 4,y_1=-8,x_2 = 8,y_2=-4 \) into the formula:
\( d=\sqrt{(8 - 4)^2+(-4+8)^2} \)

Step3: Simplify the expression inside the square root

First, calculate \( (8 - 4)^2=4^2 = 16 \) and \( (-4 + 8)^2=4^2=16 \)
Then \( d=\sqrt{16+16}=\sqrt{32} \)

Step4: Simplify the radical

\( \sqrt{32}=\sqrt{16\times2}=4\sqrt{2} \)

Answer:

\( 4\sqrt{2} \)