Video Transcript
A triangle graphed on the coordinate
plane has a vertex at six, zero. Which of the following rotations would
move the vertex to the point zero, six? Option (A) 90 degrees clockwise around
the origin. Option (B) 90 degrees counterclockwise
around the origin. Or option (C) 180 degrees clockwise or
counterclockwise around the origin.
We could start this question by sketching
out where the original vertex would be. We’re told that this vertex is at six,
zero. Let’s call this original vertex 𝐴. The image of this vertex after the
rotation is at zero, six. Let’s call this 𝐴 prime. So how would we describe the rotation
from 𝐴 to 𝐴 prime? We can recall that, to describe a
rotation, we need to say three things, the angle, the direction, and the center of
rotation. If we were to draw the angle between 𝐴
and 𝐴 prime, we would see that there’s a right angle of 90 degrees.
In terms of the direction, the direction
that’s opposite to the one in which the hands turn on a clock is called counterclockwise,
and that’s the direction that we can see here. The center of rotation will be the origin
or the coordinate zero, zero. To put these three pieces of information
together, we would say that this is a rotation of 90 degrees counterclockwise around the
origin. But there is one other way in which we
could have performed this rotation. And that is that we could have gone from
vertex 𝐴 to 𝐴 prime by going in the opposite direction through an angle of 270
degrees.
Here, the center of rotation would have
stayed the same, but we would have described the rotation as a 270-degree clockwise rotation
around the origin. However, out of these two descriptions,
only one appears in our answer options. And that is the one given in option (B),
a rotation of 90 degrees counterclockwise around the origin.
