Question
What two transformations were completed to move triangle A(-5,2) B(-3,2) C(-3,5) to triangle X(0,-6) Y(0,-4) Z(-3,-4)? Include the name of the transformation and by how much. Example- it was Rotated by 180 degrees and reflected over line x=y
Answers
GPT-4o mini
To determine the transformations that moved triangle A(-5,2) B(-3,2) C(-3,5) to triangle X(0,-6) Y(0,-4) Z(-3,-4), we can analyze the changes in coordinates.
1. **Translation**:
- To move triangle ABC to the left 5 units and down 8 units.
- The transformation can be described as:
\[
\text{Translation} \left( x \to x + 5, \, y \to y - 8 \right)
\]
- For example:
- A(-5, 2) translates to A' (0, -6)
- B(-3, 2) translates to B' (2, -6)
- C(-3, 5) translates to C' (2, -3)
2. **Reflection**:
- After this translation, we can see triangle ABC was then reflected over the line y = -4.
- The reflection of points (for example) involved making the y-coordinates become negative.
- The transformation can be described as:
\[
\text{Reflection over } y = -4
\]
Thus, the transformations that moved triangle A(-5,2) B(-3,2) C(-3,5) to triangle X(0,-6) Y(0,-4) Z(-3,-4) are:
1. Translated by (5, -8)
2. Reflected over the line \( y = -4 \)
1. **Translation**:
- To move triangle ABC to the left 5 units and down 8 units.
- The transformation can be described as:
\[
\text{Translation} \left( x \to x + 5, \, y \to y - 8 \right)
\]
- For example:
- A(-5, 2) translates to A' (0, -6)
- B(-3, 2) translates to B' (2, -6)
- C(-3, 5) translates to C' (2, -3)
2. **Reflection**:
- After this translation, we can see triangle ABC was then reflected over the line y = -4.
- The reflection of points (for example) involved making the y-coordinates become negative.
- The transformation can be described as:
\[
\text{Reflection over } y = -4
\]
Thus, the transformations that moved triangle A(-5,2) B(-3,2) C(-3,5) to triangle X(0,-6) Y(0,-4) Z(-3,-4) are:
1. Translated by (5, -8)
2. Reflected over the line \( y = -4 \)