Question

question
find the distance between the two points in simplest radical form.
(-5,-4) and (-2,-6)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-5,-4)\) and \((x_2,y_2)=(-2,-6)\)

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

Substitute the values: \(d=\sqrt{(-2-(-5))^2+(-6 - (-4))^2}\)

Step3: Simplify the expressions inside the square root

\(-2-(-5)=-2 + 5=3\) and \(-6-(-4)=-6 + 4=-2\)
So \(d=\sqrt{3^2+(-2)^2}\)

Step4: Calculate the squares

\(3^2 = 9\) and \((-2)^2=4\)
Then \(d=\sqrt{9 + 4}\)

Step5: Add the numbers inside the square root

\(9+4 = 13\)
So \(d=\sqrt{13}\)

Answer:

\(\sqrt{13}\)