Question

question
find the distance between the two points in simplest radical form.
$(-7,-8)$ and $(-2,-1)$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-7,-8)\) and \((x_2,y_2)=(-2,-1)\)

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

Substitute the values: \(x_2 - x_1=-2-(-7)=5\), \(y_2 - y_1=-1-(-8)=7\)
So \(d=\sqrt{(5)^2+(7)^2}\)

Step3: Calculate the squares

\(5^2 = 25\), \(7^2=49\)
Then \(d=\sqrt{25 + 49}\)

Step4: Add the numbers inside the square - root

\(25+49 = 74\)
So \(d=\sqrt{74}\)

Answer:

\(\sqrt{74}\)