### 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.