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What two rigid transformations were performed on figure ABCD to produce the congruent figure WXYZ ? (1 point) Responses ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise). upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated 90 degrees (counterclockwise). ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise). upper A upper B upper C upper D was first shifted 3 units to the left and 5 units up, then rotated negative 90 degrees (clockwise). ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up. upper A upper B upper C upper D was first rotated 90 degrees (counterclockwise), then shifted 3 units to the left and 5 units up. ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.

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To determine the correct sequence of transformations that produce congruent figures ABCD and WXYZ, we need to analyze the given options based on the properties of rigid transformations.

  1. Translation (shifting): This movement slides the figure in a given direction without changing its shape or orientation.
  2. Rotation: This turns the figure around a specific point by a certain angle.

Now let’s examine the options:

  • Option 1: ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
  • Option 2: ABCD was first shifted 3 units to the left and 5 units up, then rotated −90° (clockwise).
  • Option 3: ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
  • Option 4: ABCD was first rotated −270° (clockwise), then shifted 3 units to the left and 5 units up.

To find which option accurately describes the transformation that produces figure WXYZ from figure ABCD, we need to consider the impact of both translation and rotation:

  • If the first transformation is a translation followed by a rotation, it would alter the position and orientation of the figure appropriately and is commonly used in congruent transformations.

  • Similarly, if we rotate first followed by a translation, it also can yield congruency depending on the specifics of the figures involved.

Considering these insights:

Option 1 or 2 (translation first, then rotation) would typically maintain congruence, but we have to consider the direction of the rotation too.

In your case, we can't see the figures directly, but generally:

  • If you're shifting (translating) a figure (3 units left, 5 units up) and then rotating it 90 degrees counterclockwise, that's a common transformation path.

Therefore, the most typical sequence to maintain congruency would often be option 1: "ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise)."

If your figures and their requirements indicate a different sequence, that might alter the response, but elsewhere in rigid transformations, this response tends to hold.