Question

find the distance between the pair of points (0, - 4) and (6,2). if necessary, express the answer in simplified radical form and then round to two decimal places. the distance between the given points is $6\sqrt{2}$ 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 given points is approximately units. (type an integer or decimal rounded to two decimal places as needed.) b. the exact simplified form does not contain radicals.

Explanation:

Step1: Calculate the approximate value of $\sqrt{2}$

We know that $\sqrt{2}\approx1.4142$

Step2: Multiply by 6

Since the distance is $6\sqrt{2}$, then $6\times1.4142 = 8.4852$

Step3: Round to two decimal places

Rounding $8.4852$ to two decimal places, we look at the third decimal digit. The third decimal digit is 5. Using the rounding rule (if the third decimal digit is 5 or more, we round up the second decimal digit), so $8.4852\approx8.49$

Answer:

A. The distance between the given points is approximately $8.49$ units.