figure abcdef was reflected across the line $y = -x$ to create figure abcdef.

what are the coordinates of the pre-image of f?

$(-2, 4)$
$(4, 2)$
$(2, -4)$
$(-4, -2)$

Question

figure abcdef was reflected across the line $y = -x$ to create figure abcdef.

what are the coordinates of the pre-image of f?

$(-2, 4)$
$(4, 2)$
$(2, -4)$
$(-4, -2)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Coordinate Reflections", "Pre-image Coordinates", "Reflection Across y=-x" ], "current_concepts": [ "Coordinate Reflections", "Pre-image Coordinates", "Reflection Across y=-x" ] } ## Identify coordinates of the image point $F'$ $$ F' = (4, -2) $$ ## Apply the inverse reflection rule across $y = -x$ $$ \begin{aligned} &(x, y) ightarrow (-y, -x) \ &F = (-(-2), -(4)) \ &F = (2, -4) \end{aligned} $$ ## Verify the pre-image coordinates $$ F = (2, -4) $$

(-2, 4)

(4, 2)

(2, -4)

(-4, -2)

{ "elements": [ { "type": "functiongraph", "params": [{"js": "-x", "latex": "y = -x"}, -10, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 1.5, "dash": 2, "name": "y = -x", "withLabel": true } }, { "type": "point", "params": [[4, -2]], "properties": { "name": "F'(4, -2)", "size": 4, "color": "#8C55F2", "strokeColor": "#8C55F2", "fillColor": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, -4]], "properties": { "name": "F(2, -4)", "size": 4, "color": "#5583F2", "strokeColor": "#5583F2", "fillColor": "#5583F2", "withLabel": true } }, { "type": "segment", "params": [[4, -2], [2, -4]], "properties": { "strokeColor": "#55DDF2", "strokeWidth": 1, "dash": 1 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Reflections" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of the image point \(F'\)

Apply the inverse reflection rule across \(y = -x\)

Verify the pre-image coordinates

Answer: