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

(1,5) and (5,2)

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.

Question

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

(1,5) and (5,2)

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.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Radical Simplification" ] } ## Identify the given points and formula $$ \begin{aligned} &(x_1, y_1) = (1, 5)\ &(x_2, y_2) = (5, 2)\ &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{aligned} $$ ## Calculate the distance $$ \begin{aligned} &d = \sqrt{(5 - 1)^2 + (2 - 5)^2}\ &d = \sqrt{4^2 + (-3)^2}\ &d = \sqrt{16 + 9}\ &d = \sqrt{25}\ &d = 5 \end{aligned} $$ ## Determine the decimal approximation and radical status $$ \begin{aligned} &\text{Exact distance} = 5\ &\text{The exact simplified form does not contain radicals.} \end{aligned} $$ The distance between the points is 5 units. The exact simplified form does not contain radicals. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given points and formula

Calculate the distance

Determine the decimal approximation and radical status

Answer: