Question

find the distance between the two points in simplest radical form. (-5, -4) and (3, -7)

Explanation:

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1=-5\), \(y_1 = - 4\), \(x_2=3\), \(y_2=-7\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=3-(-5)=3 + 5=8\)
\(y_2 - y_1=-7-(-4)=-7 + 4=-3\)

Then, substitute these into the distance formula:
\(d=\sqrt{(8)^2+(-3)^2}\)

Step3: Simplify the expression inside the square root

Calculate the squares:
\(8^2 = 64\) and \((-3)^2=9\)
So, \(d=\sqrt{64 + 9}=\sqrt{73}\)

Answer:

\(\sqrt{73}\)