Transformations – Shortest Sequence

Directions: What is the fewest number of transformations needed to take pre-image ABCD to image A’B’C’D’?


What transformations do you need to use? Can you use the same transformations and do it another way?


A single reflection across a line that is roughly parallel to line segment DA in the pre-image will do it in one move. Otherwise students will likely get it in 2 moves by using a rotation and a reflection.

Source: Robert Kaplinsky

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  1. A reflection that takes A to A’ can only be in the perpendicular bisector of AA’
    Same goes for B and B’ and these two lines are not the same. So no single reflection.
    Maybe they put in the wrong diagram?

  2. Chelsea McClellan

    I should state that the actual location is irrelevant then. Not stating that would create major confusion.

  3. Its kind of unclear what its asking, but if it means orientation then reflect across line AD

  4. You could rotate the pre imagine until it looks like a mirror image of shape A’B’C’D’, then a reflection between the two images.

  5. A reflection across the middle of the two shapes that’s vertical and then a rotation 90 degrees clockwise

  6. I agree with Uma. 2 transformations: reflection and a rotation. After being reflected across some line parallel to AD, you will get a similar orientation. But if you bring the reflected figure of the pre-image to the image so that point B of the reflected pre-image coincide with point B’ of the image, you will see clearly that the reflected pre-image still needs to be rotated counterclockwise so that the pre-image and the image will coincide. The actual location is not relevant since that only involves some sort of translation. Maybe to be clear, the instruction should state that the image and and pre-image will have the SAME ORIENTATION.

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