what are the coordinates of the image of vertex f after a reflection across the line $y = -x$?

$(-1, -3)$
$(3, -1)$
$(1, 3)$
$(-3, 1)$

Question

what are the coordinates of the image of vertex f after a reflection across the line $y = -x$?

$(-1, -3)$
$(3, -1)$
$(1, 3)$
$(-3, 1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Coordinate Transformations" ], "new_concepts": [], "current_concepts": [ "Coordinate Transformations", "Reflection" ] } ## Identify coordinates of vertex F $$ F = (1, -3) $$ ## Apply reflection rule across $y = -x$ $$ (x, y) ightarrow (-y, -x) $$ ## Calculate image coordinates $$ \begin{aligned} x' &= -(-3) = 3 \ y' &= -(1) = -1 \ F' &= (3, -1) \end{aligned} $$

(-1, -3)

(3, -1)

(1, 3)

(-3, 1)

{ "elements": [ { "type": "point", "params": [[1, -3]], "properties": { "name": "F(1, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[3, -1]], "properties": { "name": "F'(3, -1)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-x", "latex": "y = -x"}, -10, 10], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "dash": 2 } }, { "type": "polygon", "params": [[-1, -5], [1, -3], [-2, -3], [2, -5]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 1 } } ], "timestamps": [0.5, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of vertex F

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

Calculate image coordinates

Answer: