Question

find the length of the segment connecting (0, 1) and (-6, -2). provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(-6,-2)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-6 - 0)^2+(-2 - 1)^2}\)

Step3: Simplify the expression inside the square root

\((-6 - 0)^2=(-6)^2 = 36\) and \((-2 - 1)^2=(-3)^2 = 9\)
So \(d=\sqrt{36 + 9}=\sqrt{45}\)

Step4: Calculate the square - root and round

\(\sqrt{45}\approx6.7\)

Answer:

\(6.7\)