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.