Question

what is the distance between $(-9, -6)$ and $(-2, -2)$?
choose 1 answer:
a $sqrt{28}$
b $sqrt{33}$
c $sqrt{65}$
d $sqrt{121}$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-9,-6)\) and \((x_2,y_2)=(-2,-2)\)

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

Substitute the values: \(x_2 - x_1=-2-(-9)=-2 + 9 = 7\), \(y_2 - y_1=-2-(-6)=-2 + 6 = 4\)

Step3: Calculate the distance

\(d=\sqrt{(7)^2+(4)^2}=\sqrt{49 + 16}=\sqrt{65}\)

Answer:

C. \(\sqrt{65}\)