Which transformation will be equivalent to rotating a figure 270° counterclockwise?
A) reflecting over the x-axis and the y-axis
B) translating left 3 units and down 5 units
C) Reflecting over the y-axis and then reflecting over the line y = x
D) Reflecting over the y-axis and then reflecting over the line y = -x
I think It's C
To determine the transformation that is equivalent to rotating a figure 270° counterclockwise, let's break down the options:
A) Reflecting over the x-axis and the y-axis: This transformation involves changing the signs of the x and y coordinates. It does not involve rotation and thus is not equivalent to a 270° counterclockwise rotation.
B) Translating left 3 units and down 5 units: This transformation involves shifting the figure horizontally and vertically. It does not involve rotation and therefore is not equivalent to a 270° counterclockwise rotation.
C) Reflecting over the y-axis and then reflecting over the line y = x: This sequence of transformations involves first reflecting the figure over the y-axis and then reflecting it over the line y = x. This is not equivalent to a 270° counterclockwise rotation, so option C is incorrect.
D) Reflecting over the y-axis and then reflecting over the line y = -x: This sequence of transformations involves first reflecting the figure over the y-axis and then reflecting it over the line y = -x. This is indeed equivalent to a 270° counterclockwise rotation.
Therefore, the correct answer is option D) reflecting over the y-axis and then reflecting over the line y = -x.