Question

1. (0 points) find the distance between the points \\((-8,0)\\) and \\((-4,-4)\\)

distance:

Explanation:

Step1: Identify coordinates

Identify points \((x_1, y_1) = (-8, 0)\) and \((x_2, y_2) = (-4, -4)\).

Step2: Apply distance formula

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

$$d = \sqrt{(-4 - (-8))^2 + (-4 - 0)^2}$$

Step3: Simplify terms

Simplify the differences inside the square root.

$$d = \sqrt{(4)^2 + (-4)^2}$$

Step4: Calculate squares

Calculate the squares of the simplified terms.

$$d = \sqrt{16 + 16}$$

Step5: Find final distance

Add the values and simplify the radical.

$$d = \sqrt{32} = 4\sqrt{2}$$

Answer:

\(4\sqrt{2}\)