Question

A figure on a coordinate plane is shown.
y
7
6
5
4
3
2
1 –6 –5 –4 –3 –2 0–1 –2 –3 –4 –5 –6 –7 –1 1 2 3 4 5 6–7 7
x
Select all the transformations that will map the figure onto itself.
A translation up 4 units
B reflection across they-axis
C dilation by a factor of 3 about the origin
D rotation 90 degrees clockwise about the origin
E rotation 180 degrees counterclockwise about the origin

Answer 1

To determine which transformations will map the figure onto itself, we need to consider each transformation option one by one:

A) **Translation up 4 units**: This will move every point of the figure up by 4 units. Therefore, the figure will not map onto itself and this option is **not correct**.

B) **Reflection across the y-axis**: Reflecting the figure across the y-axis means that all points will swap their x-coordinates to their negatives. If the figure is symmetric concerning the y-axis, it will map onto itself. If it is not symmetric about the y-axis, this will not hold. We cannot conclusively say that this transformation will map the figure onto itself without seeing the specific figure.

C) **Dilation by a factor of 3 about the origin**: Dilation increases the size of the figure. Thus, the figure will not map onto itself as its dimensions will change. This option is **not correct**.

D) **Rotation 90 degrees clockwise about the origin**: Rotating the figure by 90 degrees clockwise will generally change its orientation unless it has certain symmetrical properties that allow it to map onto itself. Thus, this option is likely **not correct**, but again, it depends on the specific figure.

E) **Rotation 180 degrees counterclockwise about the origin**: Rotating the figure 180 degrees will often map a figure onto itself, especially if it has rotational symmetry. This is a common transformation for many geometric figures, so it's likely that this option is **correct**, but relies on the figure's specific characteristics.

In conclusion:
- B and E are potential candidates that could map the figure onto itself, depending on the figure's symmetry properties.
- A, C, and D are confirmed as **not correct**.

If you need to be more specific about the answer based on the figure you are referring to, please provide more details about the figure's shape or symmetry.