Question

question
find the distance between the two points in simplest radical form.
(-4,-6) and (2,-1)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-4,-6)\) and \((x_2,y_2)=(2,-1)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(2-(-4))^2+(-1 - (-6))^2}\)

Step3: Simplify the expressions inside the square root

\(2-(-4)=2 + 4=6\) and \(-1-(-6)=-1 + 6 = 5\)
So \(d=\sqrt{6^2+5^2}\)
\(6^2 = 36\) and \(5^2=25\)
Then \(d=\sqrt{36 + 25}\)

Step4: Calculate the sum inside the square root

\(36+25 = 61\)
So \(d=\sqrt{61}\)

Answer:

\(\sqrt{61}\)