Question

what is the distance between a and b? a(-3, -4) b(4, 5) a $sqrt{256}$ b $sqrt{32}$ c $sqrt{130}$ d $sqrt{82}$

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, $A(-3,-4)$ so $x_1=-3,y_1 = - 4$ and $B(4,5)$ so $x_2 = 4,y_2=5$.

Step2: Substitute values

$d=\sqrt{(4-(-3))^2+(5 - (-4))^2}=\sqrt{(4 + 3)^2+(5 + 4)^2}=\sqrt{7^2+9^2}$.

Step3: Calculate squares and sum

$\sqrt{7^2+9^2}=\sqrt{49 + 81}=\sqrt{130}$.

Answer:

C. $\sqrt{130}$