Question Video: Identifying a Geometric Transformation Applied to a Quadrilateral Mathematics

What kind of transformation is shown in the figure?

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Video Transcript

What kind of transformation is shown in the figure?

We’ve been given an object and its image following a transformation and asked to determine the type of transformation that has been performed. The three types of transformation we need to consider are translation, rotation, and reflection. If the transformation was a translation, then the image would be exactly the same size and shape as the object and in the same orientation. The only thing that would change is its position. However, we can see that the image does not look exactly the same as the object. It is in a different orientation. And so, this rules out a translation.

If the transformation was a rotation, then the image would be exactly the same shape and size, but in a different position and orientation. A point has been marked on the figure, so this is a possible point about which the shape has been rotated. In order for the image to appear in the correct position below the dotted line, we’d need to rotate the shape by 180 degrees about this point. But if we did so, the image of the shape would actually be in the same orientation as the object because this shape has rotational symmetry. The transformation therefore can’t be a rotation.

The final possibility is a reflection, and there is a dotted line drawn on the figure, which is a possible mirror line. We can see that corresponding vertices on the two shapes are the same distance away from this horizontal line, but in opposite directions. The shape has also been flipped, which we can see more easily if we color the corresponding sides. The pink side is originally at the top of the object and is now at the bottom of the image. But in both cases, it’s the side furthest from the mirror. We can conclude then that the type of transformation shown is a reflection in a horizontal mirror.