To determine the correct sequence of transformations that produced the congruent figure WXYZ from figure ABCD, we need to analyze the options given and the nature of rigid transformations (translations and rotations).
- Option A states that ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° counterclockwise.
- Option B states that ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up.
- Option C states that ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (clockwise).
- Option D states that ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
To identify the correct option, we need to consider how each transformation impacts the original figure:
- Translation (shifting) moves the figure without changing its size or shape.
- Rotation changes the direction of the figure but maintains size and shape.
From the options, we can analyze a hypothesis:
- If the figure was translated first, where will those points end up?
- Then, what effect does the rotation have on those new coordinates?
Without the exact coordinates or a visual of the shapes, it's challenging to conclusively determine the transformations needed. However, generally:
- If we expect that the two figures are congruent and would have the same orientation or alignment after transformations, we would consider how rotations and translations affect their layout.
For answering:
- Based on rigid transformation principles, Option C (first shifted then rotated) is legitimate since a clockwise rotation of -90° effectively positions the figure closer to matching the new axis aligned through translation.
Thus, the correct answer is likely Option C: ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (clockwise).
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