Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal pla
(0,0) and (-3,4)
the distance between the points is 5 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 units.
(type an integer or decimal rounded to two decimal places as needed.)
○ b. the exact simplified form does not contain radicals.

Explanation:

Step1: Identify the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1 = 0,x_2=-3,y_2 = 4\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(-3 - 0)^2+(4 - 0)^2}=\sqrt{(- 3)^2+4^2}\).

Step3: Simplify the expression inside the radical

Calculate \((-3)^2 = 9\) and \(4^2=16\). Then \(d=\sqrt{9 + 16}=\sqrt{25}\).

Step4: Evaluate the square - root

Since \(\sqrt{25}=5\), the exact value of the distance is \(5\) units. As \(5\) is an integer (not a radical in simplified form), we use the fact that for an exact non - radical answer, we choose the option related to non - radical exact form.

Answer:

B. The exact simplified form does not contain radicals.