Draw transformed figures and specify transformation sequences mapping one figure to another.
Find a rigid-motion sequence mapping one figure to another
Problem
Infer the \(\text{single}\) motion from this allowed \(\text{one}\text{-}\text{step}\) family: \(\text{one}\) translation, \(\text{one}\) reflection across a coordinate axis, or \(\text{one}\) \(90°/180°/270°\) rotation about the origin. It maps \(A(0,0)\), \(B(2,0)\), \(C(0,1)\) to \(A^{\prime}(3,-2)\), \(B^{\prime}(5,-2)\), \(C^{\prime}(3,-1)\). Give the motion, coordinate rule, and checks of \(\text{all}~\text{three}~\text{mappings}\).
To infer one motion from a restricted family, compare corresponding coordinates before naming the transformation. Compute image minus source for every labeled pair: a constant difference signals one common displacement, while sign changes or coordinate swaps would signal the other allowed rules; verify all pairs before writing the general map.
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