Question

Find the distance between the pair of points (3,5) and (7,9). If necessary, express the answer in simplified radical form and then

round to two decimal places.
The distance between the given points is 4√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.

Answer 1

Explanation:

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane can be calculated using the distance formula:

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

For the given points (3, 5) and (7, 9), the distance is:

\[d = \sqrt{(7 - 3)^2 + (9 - 5)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}\]

So, the exact simplified distance is \(4\sqrt{2}\) units.

Now, let's round this to two decimal places:

\[4\sqrt{2} \approx 5.66\]

So, the answer is approximately 5.66 units.

The correct choice is A:

A. The distance between the given points is approximately 5.66 units.