find the distance between the two points.

$(-6,6)$ and $(39, -194)$

the distance is $\square$.
(type an exact answer, using radicals as needed.)

Question

find the distance between the two points.

$(-6,6)$ and $(39, -194)$

the distance is $\square$.
(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", "Coordinate Distance" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Distance" ] } ## Identify the coordinates of the two points $$ (x_1, y_1) = (-6, 6),\quad (x_2, y_2) = (39, -194) $$ ## Apply the distance formula $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ d &= \sqrt{(39 - (-6))^2 + (-194 - 6)^2} \ d &= \sqrt{(45)^2 + (-200)^2} \end{aligned} $$ ## Calculate the final distance value $$ \begin{aligned} d &= \sqrt{2025 + 40000} \ d &= \sqrt{42025} \ d &= 205 \end{aligned} $$ Find the distance between the two points. $(-6,6)$ and $(39, -194)$ The distance is 205. (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 coordinates of the two points

Apply the distance formula

Calculate the final distance value

Answer: