Question

find the distance between the two points in simplest radical form. (-9,9) and (0,-3)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-9,9)\) and \((x_2,y_2)=(0,-3)\).

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(d=\sqrt{(0-(-9))^2+(-3 - 9)^2}\).

Step3: Simplify the expressions inside the square root

\(0-(-9)=9\) and \(-3 - 9=-12\).
So \(d=\sqrt{9^2+(-12)^2}\).
\(9^2 = 81\) and \((-12)^2=144\).
Then \(d=\sqrt{81 + 144}\).
\(81+144 = 225\).

Step4: Calculate the square root

\(d=\sqrt{225}=15\).

Answer:

\(15\)