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

$(0,0)$ and $(8,-6)$

the distance between the points is $\square$ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Question

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

$(0,0)$ and $(8,-6)$

the distance between the 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": true, "concepts_used": [ "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Distance Formula" ] } ## Identify the coordinates of the points $$ (x_1, y_1) = (0, 0),\quad (x_2, y_2) = (8, -6) $$ ## Apply the distance formula $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ ## Calculate the final value $$ \begin{aligned} d &= \sqrt{(8 - 0)^2 + (-6 - 0)^2} \ d &= \sqrt{8^2 + (-6)^2} \ d &= \sqrt{64 + 36} \ d &= \sqrt{100} \ d &= 10 \end{aligned} $$ The distance between the points is 10 units. { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "(0,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[8, -6]], "properties": { "name": "(8,-6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "segment", "params": [[0, 0], [8, -6]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3, "name": "d = 10", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the points

Apply the distance formula

Calculate the final value

Answer: