Explanation:
To determine which series of transformations will not map figure L onto itself, we need to consider the properties of the figure and how transformations affect it. Figure L has four sides with vertices at the following coordinates:
(0, 1)
(3, 4)
(5, 2)
(2, -1)
Let's consider a few series of transformations:
A. Translation: (x+2, y-3) followed by Reflection over the y-axis
If you apply a translation of (x+2, y-3) followed by a reflection over the y-axis, figure L would still map onto itself. The translation shifts the figure by 2 units to the right and 3 units down, but the relative positions of the vertices remain the same. The reflection over the y-axis preserves the structure of the figure.
B. Rotation of 90 degrees counterclockwise followed by Translation: (x+2, y-3)
This series of transformations would not map figure L onto itself. The 90-degree counterclockwise rotation would change the orientation of the figure, and the subsequent translation would further shift it. The resulting figure would not be congruent to figure L.
C. Dilation with a scale factor of 2 centered at the origin
This series of transformations would not map figure L onto itself. A dilation with a scale factor of 2 centered at the origin would enlarge the figure, making it significantly larger and changing its proportions. The resulting figure would not be congruent to figure L.
Answer:
Option B and C