Problem

Reflect \((1,~3)\), \((2,~5)\), and \((4,~9)\) across \(y~=~x\). State the rule, show each mapping, and list the inverse points.

Prompt coordinate plot of original points (1,3), (2,5), and (4,9) together with y=x; all reflected points are withheld.

Big Picture

What this problem is really about

Reflection across y equals x reverses input and output roles, so every ordered pair is transformed by exchanging its coordinates. Apply that same rule consistently to each point; neither coordinate is negated. Thinking of the line y equals x as the mirror also explains why domain and range, along with horizontal and vertical features, exchange roles for inverse graphs.

Answer choices

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Preview only

Rule: reflect across the x-axis by negating y. Mappings: (1,3)→(1,−3), (2,5)→(2,−5), and (4,9)→(4,−9). Resulting points: (1,−3), (2,−5), and (4,−9).

Rule: reflect across y=x by swapping coordinates. Mappings: (1,3)→(3,1), (2,5)→(5,2), and (4,9)→(9,4). Inverse points: (3,1), (5,2), and (9,4).

Rule: keep coordinates in their original order. Mappings: (1,3)→(1,3), (2,5)→(2,5), and (4,9)→(4,9). Resulting points: (1,3), (2,5), and (4,9).

Rule: reflect across the y-axis by negating x. Mappings: (1,3)→(−1,3), (2,5)→(−2,5), and (4,9)→(−4,9). Resulting points: (−1,3), (−2,5), and (−4,9).

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Reflect \((1,~3)\), \((2,~5)\), and \((4,~9)\) across \(y~=~x\). State the rule, show each mapping, and list the inverse points.

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