Question

given a (5, -3) and b (-7, -4), which of the following is the correct setup to find the distance between these two points?
a ab = \sqrt{(5 - (-3))^{2}+(-7 - (-4))^{2}}
b ab = \sqrt{(-3 - (-7))^{2}+(5 - (-4))^{2}}
c ab = \sqrt{(-7 - 5)^{2}+(-4 - (-3))^{2}}
d ab = \sqrt{(-4 - 5)^{2}+(-7 - (-3))^{2}}
a
b
c
d

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Given $A(5,-3)$ where $x_1 = 5,y_1=-3$ and $B(-7,-4)$ where $x_2=-7,y_2 = - 4$.

Step2: Substitute values

Substitute the values into the formula: $AB=\sqrt{(-7 - 5)^2+(-4-(-3))^2}$.

Answer:

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