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.
-
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)
-
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:
- Translated by (5, -8)
- Reflected over the line \( y = -4 \)