rectangle tuvw is on a coordinate plane at t(a, b), u(a + 2, b + 2), v(a + 5, b - 1), and w(a + 3, b - 3). what is the slope of the line that is parallel to the line that contains side wv?

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Question

rectangle tuvw is on a coordinate plane at t(a, b), u(a + 2, b + 2), v(a + 5, b - 1), and w(a + 3, b - 3). what is the slope of the line that is parallel to the line that contains side wv?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel Lines" ], "new_concepts": [ "Slope Formula" ], "current_concepts": [ "Parallel Lines", "Properties of Rectangles", "Slope Formula" ] } ## Calculate the slope of side WV $$ \begin{aligned} &W = (a + 3, b - 3),\quad V = (a + 5, b - 1)\ &m_{WV} = \frac{(b - 1) - (b - 3)}{(a + 5) - (a + 3)} = \frac{2}{2} = 1 \end{aligned} $$ ## Determine the slope of a parallel line $$ \begin{aligned} &m_{\text{parallel}} = m_{WV} = 1 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines" ] }

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Explanation:

Calculate the slope of side WV

Determine the slope of a parallel line

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