find the distance between each pair of points. leave your answer in square root form. type your answer in the form sqrt(...)

distance =

Question

find the distance between each pair of points. leave your answer in square root form. type your answer in the form sqrt(...)

distance =

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Geometry", "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Coordinate Geometry", "Distance Formula" ] } ## Identify the coordinates of the endpoints from the graph $$ \begin{aligned} &(x_1, y_1) = (2, 3)\ &(x_2, y_2) = (4, -3) \end{aligned} $$ ## Apply the distance formula $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\ d &= \sqrt{(4 - 2)^2 + (-3 - 3)^2}\ d &= \sqrt{2^2 + (-6)^2}\ d &= \sqrt{4 + 36}\ d &= \sqrt{40} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} d &= \sqrt{4 \times 10}\ d &= 2\sqrt{10} \end{aligned} $$ Find the distance between each pair of points. Leave your answer in square root form. Type your answer in the form sqrt(...) with no spaces. Distance = sqrt(40) { "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 endpoints from the graph

Apply the distance formula

Simplify the radical expression

Answer: