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: Recall 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, $x_1=-9,y_1 = - 6,x_2=-2,y_2=-2$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-2-(-9)=-2 + 9 = 7$, $y_2 - y_1=-2-(-6)=-2 + 6 = 4$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(7)^2+(4)^2}=\sqrt{49 + 16}=\sqrt{65}$.

Answer:

C. $\sqrt{65}$