Question

question 2 · 1 point
find the distance between the points (-6,8) and (-5,1).
give an exact answer in simplest radical form. do not round.
provide your answer below:

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, $x_1=-6,y_1 = 8,x_2=-5,y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(-5-(-6))^2+(1 - 8)^2}=\sqrt{(-5 + 6)^2+(1 - 8)^2}=\sqrt{(1)^2+(-7)^2}$.

Step3: Calculate squares and sum

$\sqrt{1 + 49}=\sqrt{50}$.

Step4: Simplify radical

$\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$