Question

find the distance between the points (4, -2) and (0, -9). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify the distance formula

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

Step2: Assign the values of the points

Let $(x_1,y_1)=(4,-2)$ and $(x_2,y_2)=(0,-9)$. Then $x_1 = 4$, $y_1=-2$, $x_2 = 0$, $y_2=-9$.

Step3: Substitute values into the formula

$d=\sqrt{(0 - 4)^2+(-9-(-2))^2}=\sqrt{(-4)^2+(-9 + 2)^2}=\sqrt{16+(-7)^2}$.

Step4: Simplify the expression

$d=\sqrt{16 + 49}=\sqrt{65}$.

Answer:

$\sqrt{65}$