a line segment has endpoints at $(-1, 4)$ and $(4, 1)$. which reflection will produce an image with endpoints at $(-4, 1)$ and $(-1, -4)$?

a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line $y = x$
a reflection of the line segment across the line $y = -x$

Question

a line segment has endpoints at $(-1, 4)$ and $(4, 1)$. which reflection will produce an image with endpoints at $(-4, 1)$ and $(-1, -4)$?

a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line $y = x$
a reflection of the line segment across the line $y = -x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Transformations", "Reflection Properties" ], "new_concepts": [], "current_concepts": [ "Coordinate Transformations", "Reflection Properties", "Reflection across y=x" ] } ## Identify the mapping of the endpoints $$ \begin{aligned} A(-1, 4) & ightarrow A'(-4, 1) \ B(4, 1) & ightarrow B'(-1, -4) \end{aligned} $$ ## Determine the coordinate transformation rule $$ (x, y) ightarrow (-y, -x) $$ ## Match the rule to the geometric reflection $$ \text{Reflection across the line } y = -x $$

a reflection of the line segment across the x-axis

a reflection of the line segment across the y-axis

a reflection of the line segment across the line y = x

a reflection of the line segment across the line y = -x

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the mapping of the endpoints

Determine the coordinate transformation rule

Match the rule to the geometric reflection

Answer: