Question

Triangle A’B’C’ is the image of triangle ABC.

On a coordinate plane, triangle A B C has points negative 4, negative 1), (negative 5, negative 5), (negative 3, negative 4). Triangle A prime B prime C prime has points (3, 4), (4, 8), (2, 7).

Which transformations could have been used to create A’B’C’ ? Choose all that apply.
a 180degree rotation about the origin and then a translation 3 units up and 1 unit left
a translation 3 units up and 1 unit left and then a 180degree rotation about the origin
a 90degree clockwise rotation about the origin and then a reflection over the y-axis
a 90degree counterclockwise rotation about the origin and then a reflection over the x-axis
a translation 3 units down and 1 unit right and then a 180degree rotation about the origin

Hurry Quick i need the answer ASAP

Answer 1

Answer:Let's analyze the possible transformations:

1. **180-degree rotation about the origin and then a translation 3 units up and 1 unit left:**

  - This would alter both the rotation and translation, so it's a potential transformation.

2. **Translation 3 units up and 1 unit left and then a 180-degree rotation about the origin:**

  - This is similar to the first option but in reverse order. It should yield the same result, so it's a potential transformation.

3. **90-degree clockwise rotation about the origin and then a reflection over the y-axis:**

  - This sequence of transformations is not likely to match the given points.

4. **90-degree counterclockwise rotation about the origin and then a reflection over the x-axis:**

  - This sequence of transformations is not likely to match the given points.

5. **Translation 3 units down and 1 unit right and then a 180-degree rotation about the origin:**

  - This would alter both the translation and rotation, so it's a potential transformation.

Based on the analysis, the correct transformations are:

- **a 180-degree rotation about the origin and then a translation 3 units up and 1 unit left**

- **a translation 3 units up and 1 unit left and then a 180-degree rotation about the origin**

- **a translation 3 units down and 1 unit right and then a 180-degree rotation about the origin**

These three sequences could potentially result in the transformation from triangle ABC to A'B'C'.

Step-by-step explanation:Let's analyze the possible transformations:

1. **180-degree rotation about the origin and then a translation 3 units up and 1 unit left:**

  - This would alter both the rotation and translation, so it's a potential transformation.

2. **Translation 3 units up and 1 unit left and then a 180-degree rotation about the origin:**

  - This is similar to the first option but in reverse order. It should yield the same result, so it's a potential transformation.

3. **90-degree clockwise rotation about the origin and then a reflection over the y-axis:**

  - This sequence of transformations is not likely to match the given points.

4. **90-degree counterclockwise rotation about the origin and then a reflection over the x-axis:**

  - This sequence of transformations is not likely to match the given points.

5. **Translation 3 units down and 1 unit right and then a 180-degree rotation about the origin:**

  - This would alter both the translation and rotation, so it's a potential transformation.

Based on the analysis, the correct transformations are:

- **a 180-degree rotation about the origin and then a translation 3 units up and 1 unit left**

- **a translation 3 units up and 1 unit left and then a 180-degree rotation about the origin**

- **a translation 3 units down and 1 unit right and then a 180-degree rotation about the origin**

These three sequences could potentially result in the transformation from triangle ABC to A'B'C'.