Question

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

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-5,-4)\) and \((x_2,y_2)=(3,-7)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(3-(-5))^2+(-7 - (-4))^2}\)

Step3: Simplify the expressions inside the square - root

\(3-(-5)=3 + 5=8\) and \(-7-(-4)=-7 + 4=-3\)
So \(d=\sqrt{8^2+(-3)^2}\)

Step4: Calculate the squares

\(8^2 = 64\) and \((-3)^2=9\)
Then \(d=\sqrt{64 + 9}\)

Step5: Add the numbers inside the square - root

\(64+9 = 73\)
So \(d=\sqrt{73}\)

Answer:

\(\sqrt{73}\)