Question

Parallelogram is shown with vertices at negative 5 comma 1, negative 4 comma 3, negative 1 comma 3, and negative 2 comma 1. What series of transformations would carry the parallelogram onto itself? (x + 0, y − 6), 180° rotation, (x − 2, y − 2) (x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2) (x + 6, y + 0), 180° rotation, (x + 0, y + 4) (x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)

Answer 1

Answer: To determine the series of transformations that would carry the parallelogram onto itself, let's analyze the given options:

1. (x + 0, y − 6), 180° rotation, (x − 2, y − 2)

This option involves a translation of 0 units horizontally and -6 units vertically, followed by a 180° rotation. However, it does not match the given vertices of the parallelogram, so it cannot carry the parallelogram onto itself.

2. (x − 2, y − 2), 90° clockwise rotation, (x + 0, y − 6)

This option involves a translation of -2 units horizontally and -2 units vertically, followed by a 90° clockwise rotation. Again, it does not match the given vertices of the parallelogram, so it is not a valid series of transformations.

3. (x + 6, y + 0), 180° rotation, (x + 0, y + 4)

This option involves a translation of 6 units horizontally and 0 units vertically, followed by a 180° rotation. However, it also does not match the given vertices of the parallelogram, so it is not correct.

4. (x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)

This option involves a translation of 6 units horizontally and 0 units vertically, followed by a 90° clockwise rotation. This series of transformations matches the given vertices of the parallelogram, which means it will carry the parallelogram onto itself. Therefore, this is the correct series of transformations.

In conclusion, the series of transformations that would carry the parallelogram onto itself is:

- Translate 6 units horizontally and 0 units vertically (x + 6, y + 0)

- Perform a 90° clockwise rotation

- Translate 0 units horizontally and 4 units vertically (x + 0, y + 4)