Question

find the distance between the pair of points $(-3,-6)$ and $(3,-5)$. if necessary, express the answer in simplified radical form and then round to two decimal places.
the distance between the given points is $square$ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-3,-6)\) and \((x_2,y_2)=(3,-5)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(3-(-3))^2+(-5 - (-6))^2}\)

Step3: Simplify the expressions inside the square - root

First, \(3-(-3)=3 + 3=6\) and \(-5-(-6)=-5 + 6 = 1\)
So \(d=\sqrt{6^2+1^2}=\sqrt{36 + 1}\)

Step4: Calculate the final value

\(d=\sqrt{37}\)

Answer:

\(\sqrt{37}\)