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: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-5,y_1 = - 6,x_2=-3,y_2=-8\).

Step2: Substitute the values into the formula

First, find \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-3-(-5)=-3 + 5 = 2\)
\(y_2 - y_1=-8-(-6)=-8 + 6=-2\)
Then, \((x_2 - x_1)^2+(y_2 - y_1)^2=2^2+(-2)^2\)
\(2^2+(-2)^2 = 4 + 4=8\)
So, \(d=\sqrt{8}\)

Answer:

D. \(\sqrt{8}\)