Question

find the distance between the two points in simplest radical form. answer attempt 1 out of 2

Explanation:

Step1: Identify the points

Let the two - point be $(x_1,y_1)$ and $(x_2,y_2)$. Assume the upper - point is $(0,4)$ and the lower - right point is $(8, - 9)$.

Step2: Apply the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 0,y_1 = 4,x_2 = 8,y_2=-9$. Then $d=\sqrt{(8 - 0)^2+(-9 - 4)^2}$.

Step3: Calculate the values inside the square - root

First, $(8 - 0)^2=8^2 = 64$ and $(-9 - 4)^2=(-13)^2 = 169$. So $d=\sqrt{64 + 169}$.

Step4: Simplify the square - root

$d=\sqrt{233}$.

Answer:

$\sqrt{233}$