Question

what is the distance between $(-5, -6)$ and $(-3, -8)$?
choose 1 answer:
a 2
b 4
c $sqrt{4}$
d $sqrt{8}$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-5,-6)\) and \((x_2,y_2)=(-3,-8)\)

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

Substitute the values: \(d=\sqrt{(-3-(-5))^2+(-8 - (-6))^2}\)

Step3: Simplify the expressions inside the square - root

\(-3-(-5)=-3 + 5=2\) and \(-8-(-6)=-8 + 6=-2\)
So \(d=\sqrt{(2)^2+(-2)^2}=\sqrt{4 + 4}=\sqrt{8}\)

Answer:

D. \(\sqrt{8}\)