Question

Question was provided via image upload.

Explanation:

Identify coordinates and formula

$$ (x_1, y_1) = (5, 3),\quad (x_2, y_2) = (13, 9) $$

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Calculate the distance

$$ d = \sqrt{(13 - 5)^2 + (9 - 3)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 $$

Determine radical status

The exact distance is \(10\), which is an integer and does not contain radicals.

Answer:

The distance between the points is <blank>10</blank> units.

• A. The distance between the points is approximately <blank></blank> units.
• B. The exact simplified form does not contain radicals. (Correct answer)