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{ "quality": "incomplete", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula", "Perpendicular Slopes" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Perpendicular Slopes", "Perpendicular Chord Bisector Theorem" ] } ## Identify the geometric relationship $$ \overline{EF} \perp \overline{AB} \implies m_{\overline{EF}} \cdot m_{\overline{AB}} = -1 $$ ## Determine the slope of AB from the grid $$ \begin{aligned} &\text{Let } A = (2, 8) \text{ and } B = (6, 2)\ &m_{\overline{AB}} = \frac{2 - 8}{6 - 2} = \frac{-6}{4} = -\frac{3}{2} \end{aligned} $$ ## Calculate the perpendicular slope of EF $$ \begin{aligned} &m_{\overline{EF}} = -\frac{1}{m_{\overline{AB}}} = -\frac{1}{-\frac{3}{2}} = \frac{2}{3} \end{aligned} $$ ## Question 1 What is the slope of $\overline{AB}$? $-\frac{3}{2}$ ## Question 2 What is the slope of $\overline{EF}$? $\frac{2}{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Slopes" ] }

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Explanation:

Identify the geometric relationship

Determine the slope of AB from the grid

Calculate the perpendicular slope of EF

Answer:

Question 1

Question 2