Question

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

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

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4-(-3)=7$ and $y_2 - y_1=5 - (-4)=9$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(7)^2+(9)^2}=\sqrt{49 + 81}=\sqrt{130}$.

Answer:

C. $\sqrt{130}$