Question

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

Explanation:

Step1: Identify the coordinates

Let the two points be \( (x_1, y_1) = (-1, -3) \) and \( (x_2, y_2) = (3, -2) \).

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 the values: \( x_1 = -1 \), \( y_1 = -3 \), \( x_2 = 3 \), \( y_2 = -2 \).
First, calculate \( x_2 - x_1 = 3 - (-1) = 4 \).
Then, calculate \( y_2 - y_1 = -2 - (-3) = 1 \).
Now, substitute into the formula: \( d = \sqrt{4^2 + 1^2} = \sqrt{16 + 1} = \sqrt{17} \).

Step3: Calculate the numerical value

\( \sqrt{17} \approx 4.123 \) (rounded to three decimal places).

Answer:

\( 4.123 \)