Problem

Apply \(T(x,y)=(x,-y)\) to \(A(2,1)\), \(B(5,1)\), \(C(2,4)\), whose proposed corresponding image is \(D(2,-1)\), \(E(5,-1)\), \(F(2,-4)\). Identify the transformation, give \(\text{all}~\text{three}~\text{image}~\text{vertices}\), and determine whether \(\triangle~ABC~\cong~\triangle~DEF\).

Source data: T(x,y)=(x,-y); A(2,1),B(5,1),C(2,4); proposed D(2,-1),E(5,-1),F(2,-4).

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type = reflection across the y-axis; images = A′(-2,1), B′(-5,1), C′(-2,4); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

type = reflection across the x-axis; images = A′(2,-1), B′(5,-1), C′(2,-2); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

type = reflection across the x-axis; images = A′(2,-1), B′(5,-1), C′(2,-4), matching D,E,F; rigid = yes, all pairwise distances are preserved; conclusion = △ABC≅△DEF

type = translation by ⟨0,-2⟩; images = A′(2,-1), B′(5,-1), C′(2,2); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

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Apply \(T(x,y)=(x,-y)\) to \(A(2,1)\), \(B(5,1)\), \(C(2,4)\), whose proposed corresponding image is \(D(2,-1)\), \(E(5,-1)\), \(F(2,-4)\). Identify the transformation, give \(\text{all}~\text{three}~\text{image}~\text{vertices}\), and determine whether \(\triangle~ABC~\cong~\triangle~DEF\).

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