Question

calculate the distance between the two points.
round to three decimal places.

Explanation:

Step1: Identify the coordinates of the two points.

Let's assume the left - most point has coordinates \((x_1,y_1)=(-5, - 5)\) and the other point has coordinates \((x_2,y_2)=(-2,-3)\).

Step2: Apply the distance formula.

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1=-5,y_1 = - 5,x_2=-2,y_2=-3\) into the formula:
First, calculate \(x_2 - x_1=-2-(-5)=-2 + 5 = 3\) and \(y_2 - y_1=-3-(-5)=-3 + 5 = 2\).
Then, \(d=\sqrt{(3)^2+(2)^2}=\sqrt{9 + 4}=\sqrt{13}\).

Step3: Calculate the numerical value and round.

\(\sqrt{13}\approx3.60555\). Rounding to three decimal places, we get \(3.606\).

Answer:

\(3.606\)