Problem

Start with \((1,3)\). Sequence A translates by \(\langle~2,0\rangle\), then reflects over the \(y\text{-}\text{axis}\). Sequence B reflects over the \(y\text{-}\text{axis}\), then translates by \(\langle~2,0\rangle\). Compute \(\text{both}\) images and determine whether they are the same.

Source comparison: Start point (1,3); sequence A translates by ⟨2,0⟩ then reflects over the y-axis; sequence B reflects over the y-axis then translates by ⟨2,0⟩.

Big Picture

What this problem is really about

Having the same two transformations does not guarantee the same composition, because each second step receives a different intermediate point. Start both paths from the original coordinate, track and label each intermediate image, complete each path independently, and compare only the two final coordinates.

Answer choices

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Preview only

image A: (-3, 3); image B: (-3, 3); same image: yes

image A: (3, 3); image B: (-1, 3); same image: no

image A: (-1, 3); image B: (3, 3); same image: no

image A: (-3, 3); image B: (1, 3); same image: no

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Start with \((1,3)\). Sequence A translates by \(\langle~2,0\rangle\), then reflects over the \(y\text{-}\text{axis}\). Sequence B reflects over the \(y\text{-}\text{axis}\), then translates by \(\langle~2,0\rangle\). Compute \(\text{both}\) images and determine whether they are the same.

What this problem is really about

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