Video Transcript
Where does a rotation through 180
degrees about 𝑀 send the segment 𝐹𝐴?
Let’s remember that a rotation is
the transformation that turns a shape in a circular motion about a point. In this question, the shape is the
line segment 𝐹𝐴 and the rotation is 180 degrees about the point 𝑀. Usually, we have a direction of
motion or turn, but since 180 degrees is exactly half of a full turn of 360 degrees,
then we can achieve that in either the clockwise or the counterclockwise
direction. Let’s start with vertex 𝐴 and see
where its image would appear after a rotation of 180 degrees.
Each vertex will always be the same
distance from the center of rotation. For example, if we rotated 𝐴 60
degrees clockwise about 𝑀, then its image would appear at vertex 𝐹. We know that it would be an angle
of 60 degrees that would rotate 𝐴 to 𝐹 as we have a regular hexagon. Therefore, if we rotated 180
degrees and the direction of this arrow is clockwise, then the image of 𝐴 will be
at vertex 𝐷.
Next, we can consider where the
image of point 𝐹 would be after a 180-degree rotation. It would be here at vertex 𝐶. Therefore, we can give our answer
that a rotation of 180 degrees about 𝑀 sends the segment 𝐹𝐴 to line segment
𝐶𝐷.
