Question Video: Identifying the Type of Transformation Mathematics • 8th Grade

Sophia went on a hike in the woods. She was walking northeast along a trail. When she got to a fork in the trail, she started walking northwest. Fully describe the rotation she made at the fork in the trail.

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Video Transcript

Sophia went on a hike in the woods. She was walking northeast along a trail. When she got to a fork in the trail, she started walking northwest. Fully describe the rotation she made at the fork in the trail.

In this question, we’re told that Sophia is walking through the woods. She is walking northeast. This means that we’ll need to recall our compass directions. We always have north at the top, south at the bottom, and then west and east. As Sophia is walking northeast, then she’s walking in this direction. So, here’s Sophia walking along the trail until she gets to a fork in the trail. A fork in a trail would be a place where there are a number of different paths.

We’re told that Sophia then starts to walk Northwest. Northwest is between north and west, so Sophia starts to walk in this direction. We’re then asked to describe the rotation she made at the fork in the trail. This is the point where she changed direction. When Sophia got to the fork in the trail, she was looking in the northeast direction. Instead of continuing forward, however, she turned to the northwest direction. This turn indicates a rotation. And in order to describe a rotation, we need to give the angle of the rotation and its direction.

If we look at our compass points, the angle between north and east is a right angle of 90 degrees. Therefore, the angle between north and northeast is exactly half of this. It’s 45 degrees. The same is true for the angle between north and northwest. It’s also 45 degrees. So, when Sophia turned, she turned at an angle of 90 degrees. The direction of this turn is counterclockwise. We can, therefore, give our answer that the rotation made is a rotation by 90 degrees counterclockwise.

We could also have described this as a rotation by 270 degrees clockwise. Usually when we’re describing the rotation of a shape, we’d also need to give the point about which the shape is rotated. In this case, the center of rotation is the fork in the trail, and that was given to us in the question. Therefore, an answer of rotation by 90 degrees counterclockwise is sufficient.

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