classify quadrilateral abcd.
is it a parallelogram? find the slope of each side.
slope $\overline{ab}$ =
slope $\overline{bd}$ =
slope $\overline{cd}$ =
slope $\overline{ac}$ =

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula" ], "new_concepts": [ "Classifying Quadrilaterals on Coordinate Plane" ], "current_concepts": [ "Slope Formula", "Classifying Quadrilaterals on Coordinate Plane" ] } ## Identify the coordinates of the vertices $$ A(-4, 0),\quad B(-3, -3),\quad C(-1, 1),\quad D(0, -2) $$ ## Calculate the slopes of the opposite sides $$ \begin{aligned} &\text{Slope of } \overline{AB} = \frac{-3 - 0}{-3 - (-4)} = \frac{-3}{1} = -3\ &\text{Slope of } \overline{CD} = \frac{-2 - 1}{0 - (-1)} = \frac{-3}{1} = -3\ &\text{Slope of } \overline{AC} = \frac{1 - 0}{-1 - (-4)} = \frac{1}{3}\ &\text{Slope of } \overline{BD} = \frac{-2 - (-3)}{0 - (-3)} = \frac{1}{3} \end{aligned} $$ ## Verify the parallel sides $$ \begin{aligned} &\text{Slope of } \overline{AB} = \text{Slope of } \overline{CD} = -3 \implies \overline{AB} \parallel \overline{CD}\ &\text{Slope of } \overline{AC} = \text{Slope of } \overline{BD} = \frac{1}{3} \implies \overline{AC} \parallel \overline{BD} \end{aligned} $$ Classify Quadrilateral ABCD. Is it a parallelogram? Find the slope of each side. Slope $\overline{AB}$ = -3 Slope $\overline{BD}$ = $\frac{1}{3}$ Slope $\overline{CD}$ = -3 Slope $\overline{AC}$ = $\frac{1}{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Slope Formula" ] }

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Explanation:

Identify the coordinates of the vertices

Calculate the slopes of the opposite sides

Verify the parallel sides

Answer: