which statement best explains the relationship between lines cd and fg?

they are perpendicular because their slopes are equal
they are perpendicular because their slopes are negative reciprocals.
they are not perpendicular because their slopes are equal
they are not perpendicular because their slopes are negative reciprocals.

Question

which statement best explains the relationship between lines cd and fg?

they are perpendicular because their slopes are equal
they are perpendicular because their slopes are negative reciprocals.
they are not perpendicular because their slopes are equal
they are not perpendicular because their slopes are negative reciprocals.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Line Slopes" ], "new_concepts": [], "current_concepts": [ "Perpendicular Line Slopes", "Slope Formula" ] } ## Calculate the slope of line CD $$ \begin{aligned} &C = (-3, 3),\quad D = (-1, -5)\ &m_{CD} = \frac{-5 - 3}{-1 - (-3)} = \frac{-8}{2} = -4 \end{aligned} $$ ## Calculate the slope of line FG $$ \begin{aligned} &F = (-4, 0),\quad G = (4, 2)\ &m_{FG} = \frac{2 - 0}{4 - (-4)} = \frac{2}{8} = \frac{1}{4} \end{aligned} $$ ## Determine the relationship between the slopes $$ \begin{aligned} &m_{CD} \cdot m_{FG} = -4 \cdot \frac{1}{4} = -1 \end{aligned} $$

They are perpendicular because their slopes are equal

They are perpendicular because their slopes are negative reciprocals.

They are not perpendicular because their slopes are equal

They are not perpendicular because their slopes are negative reciprocals.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Line Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of line CD

Calculate the slope of line FG

Determine the relationship between the slopes

Answer: