Problem

Apply \(T(x,y)=(-x,y)\) to \(A(1,1)\), \(B(4,1)\), \(C(1,3)\), whose proposed corresponding image is \(D(-1,1)\), \(E(-4,1)\), \(F(-1,3)\). 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(1,1),B(4,1),C(1,3); proposed D(-1,1),E(-4,1),F(-1,3).

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type = reflection across the x-axis; images = A′(1,-1), B′(4,-1), C′(1,-3); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

type = translation by ⟨-2,0⟩; images = A′(-1,1), B′(2,1), C′(-1,3); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

type = reflection across the y-axis; images = A′(-1,1), B′(-4,-1), C′(-1,3); rigid = yes, all pairwise distances are preserved; conclusion = △ABC is not congruent to △DEF

type = reflection across the y-axis; images = A′(-1,1), B′(-4,1), C′(-1,3), matching D,E,F; rigid = yes, all pairwise distances are preserved; conclusion = △ABC≅△DEF

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Apply \(T(x,y)=(-x,y)\) to \(A(1,1)\), \(B(4,1)\), \(C(1,3)\), whose proposed corresponding image is \(D(-1,1)\), \(E(-4,1)\), \(F(-1,3)\). Identify the transformation, give \(\text{all}~\text{three}~\text{image}~\text{vertices}\), and determine whether \(\triangle~ABC~\cong~\triangle~DEF\).

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