Video Transcript
If triangle π΄π΅πΆ is rotated by π
brackets π, 90 degrees, which triangle would represent its final position?
And we are given four possible
answer options for the position of triangle π΄π΅πΆ. In this first, largest graph, we
can observe the right triangle π΄π΅πΆ with all its coordinates in the first
quadrant. And we are told that this triangle
is rotated. The π in the brackets notation
means that the rotation is performed about π, the origin, which means that the
rotation has a center of rotation at π. The value of 90 degrees indicates
that the angle of rotation is 90 degrees. And when no direction is specified
in a rotation, we use the convention that a positive angle of rotation means a
counterclockwise direction, which is what we have here.
All of the coordinates of triangle
π΄π΅πΆ are going to move 90 degrees counterclockwise and will be in the second
quadrant. That means we can straightaway tell
that the shapes in the graphs in options (A) and (D) are in the wrong quadrant. So letβs see what triangle π΄π΅πΆ
would look like after the correct rotation. We can take each of the points β
here, for example, we have point π΄ β and draw a line from the point to the center
of rotation, which is the point π. A 90 degreesβ counterclockwise
rotation would take point π΄ to here. This is the image of point π΄, and
we can label it with the notation π΄ prime. The coordinates of π΄ prime are at
negative one, one.
We can do the same with point π΅,
drawing a line from this point to the origin. A 90-degree counterclockwise turn
would create the image π΅ prime at the coordinates negative one, three. And we can do the same for point
πΆ. The rotation of 90 degrees
counterclockwise would produce the point πΆ prime at the coordinates negative two,
one. We can join the points to create
the triangle π΄ prime π΅ prime πΆ prime. This is the answer given in the
graph in option (C).
Notice that the graph in option (D)
which we already eliminated would show the rotation of triangle π΄π΅πΆ by a rotation
of 90 degrees clockwise. Or using the same notation, we
could say that this is the rotation π
about the point π by negative 90
degrees. Options (A) and (B) appear to be
reflections instead, with option (A) being a reflection in the π₯-axis and option
(B) being a reflection in the π¦-axis. So answers (A), (B), and (D) are
incorrect and only the graph in option (C) is correct.