find the distance between the pair of points $(1.3, 8.2)$ and $(-0.7, 6.2)$. 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 $(1.3, 8.2)$ and $(-0.7, 6.2)$. 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 coordinates $$ (x_1, y_1) = (1.3, 8.2),\quad (x_2, y_2) = (-0.7, 6.2) $$ ## Apply the distance formula $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ d &= \sqrt{(-0.7 - 1.3)^2 + (6.2 - 8.2)^2} \ d &= \sqrt{(-2)^2 + (-2)^2} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} d &= \sqrt{4 + 4} \ d &= \sqrt{8} \ d &= 2\sqrt{2} \end{aligned} $$ Find the distance between the pair of points $(1.3, 8.2)$ and $(-0.7, 6.2)$. If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is $2\sqrt{2}$ units. { "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 coordinates

Apply the distance formula

Simplify the radical expression

Answer: