what are the coordinates of $a$ after reflecting across the line $x = 3$?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Coordinate Transformations" ], "new_concepts": [ "Reflection Across Vertical Lines" ], "current_concepts": [ "Coordinate Transformations", "Reflection Across Vertical Lines" ] } ## Identify coordinates of point A $$ A = (3, 2) $$ ## Apply reflection rule across vertical line $$ \begin{aligned} x' &= 2h - x \ x' &= 2(3) - 3 = 3 \ y' &= y = 2 \end{aligned} $$ ## State coordinates of reflected point $$ A' = (3, 2) $$ $(3, 2)$ { "elements": [ { "type": "line", "params": [[3, -3], [3, 7]], "properties": { "name": "x = 3", "strokeColor": "#F2557F", "strokeWidth": 2, "dash": 2, "withLabel": true } }, { "type": "polygon", "params": [[3, 2], [2, 4], [6, 3], [1, 0]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [[3, 2]], "properties": { "name": "A (A')", "color": "#5583F2", "size": 4, "withLabel": true } }, { "type": "point", "params": [[2, 4]], "properties": { "name": "B", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[6, 3]], "properties": { "name": "C", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[1, 0]], "properties": { "name": "D", "color": "#8C55F2", "size": 3, "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Transformations" ] }

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Explanation:

Identify coordinates of point A

Apply reflection rule across vertical line

State coordinates of reflected point

Answer: