Question

find the distance between the points (6, 5) and (0, 0). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall 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, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(6,5)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,x_2 = 6,y_2 = 5$ into the formula: $d=\sqrt{(6 - 0)^2+(5 - 0)^2}=\sqrt{6^{2}+5^{2}}$.

Step3: Calculate squares and sum

$6^{2}=36$ and $5^{2}=25$, so $d=\sqrt{36 + 25}=\sqrt{61}$.

Answer:

$\sqrt{61}$ units