Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.

\\((0,0)\\) and \\((6,-8)\\)

the distance between the points is \\(\square\\) units.
(simplify your answer. type an exact answer, using radicals as needed.)

express the distance rounded to two decimal places if the exact simplified answer contains radicals.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the distance between the points is approximately \\(\square\\) units.
(type an integer or decimal rounded to two decimal places as needed.)

b. the exact simplified form does not contain radicals.

Explanation:

Identify the given coordinates

Using the Distance Formula knowledge point

$$ (x_1, y_1) = (0, 0),\quad (x_2, y_2) = (6, -8) $$

Apply the distance formula

Using the Distance Formula knowledge point

$$
LATEXBLOCK0
$$

Determine the decimal approximation requirement

Since the exact simplified distance is \(10\), which is an integer, it does not contain any radicals. Therefore, the second part of the question regarding decimal approximation is not applicable, and we select option B.

Answer:

Question 1

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

Question 2

• A. The distance between the points is approximately [ ] units
• B. The exact simplified form does not contain radicals. (Correct answer)