Final answer:
The sequence of transformations applied to points involves rotations and reflections in various orders, which significantly affect the final positions of the points. Rotations turn points about a center, while reflections flip points over an axis.
Step-by-step explanation:
The sequence of transformations applied to points refers to the steps taken to move or change the points in a given space. When we apply transformations to points, it is important to consider the order in which these transformations occur as they affect the outcome.
To determine the effect of these transformations, one must first specify the coordinate system. Once this is done, a rotation is performed, which is a transformation that turns each point about a fixed center by a certain angle. A positive angle conventionally indicates a counterclockwise rotation.
A reflection is a transformation that 'flips' the points over a particular line, known as the axis of reflection. Reflecting through the horizontal-axis changes the sign of the y-coordinate of each point, whereas reflecting through the vertical-axis changes the sign of the x-coordinate of each point.
The sequence in which these transformations are applied has significant implications on the final position of the points. If you rotate first and then reflect, the final position of the points will be different compared to the scenario when you reflect first and then rotate.
To summarize the four scenario options given:
First rotate the points through radians and then reflect them through the horizontal-axis.
First reflect the points through the horizontal-axis and then rotate them through radians.
First rotate the points through radians and then reflect them through the vertical-axis.
First reflect the points through the vertical-axis and then rotate them through radians.