Question Video: Finding the Image of a Line Segment by a 180-Degree Rotation about a Point Mathematics • 8th Grade

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.