Question

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

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-6,4)\) and \((x_2,y_2)=(-8,6)\)

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

Substitute the values: \(d=\sqrt{(-8-(-6))^2+(6 - 4)^2}\)

Step3: Simplify the expression inside the square root

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

Answer:

D. \(\sqrt{8}\)