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 $\square$ units.
(simplify your answer. type an exact answer, using radicals as needed.)

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 $\square$ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "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 $$ (x_1, y_1) = (0, -4),\quad (x_2, y_2) = (6, 2) $$ ## Apply the distance formula $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ d &= \sqrt{(6 - 0)^2 + (2 - (-4))^2} \ d &= \sqrt{6^2 + 6^2} \ d &= \sqrt{36 + 36} \ d &= \sqrt{72} \end{aligned} $$ ## Simplify the radical expression $$ d = \sqrt{36 \times 2} = 6\sqrt{2} $$ The distance between the given points is $6\sqrt{2}$ units. (Simplify your answer. Type an exact answer, using radicals as needed.) { "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

Apply the distance formula

Simplify the radical expression

Answer: