To find the sequence of transformations that map triangle ΔA (-5, 2) B (-2, 4) C (-3, 0) to triangle ΔA" (-1, -2) B" (2, -4) C" (1, 0), we can analyze the movement of the points in the coordinate plane.
Step 1: Examine the coordinates of the triangles
-
Triangle ΔA is defined by the vertices:
- A (-5, 2)
- B (-2, 4)
- C (-3, 0)
-
Triangle ΔA" is defined by the vertices:
- A" (-1, -2)
- B" (2, -4)
- C" (1, 0)
Step 2: Find transformations step-by-step
First, let's see how the x-coordinates change from ΔA to ΔA":
- For A: -5 to -1 → +4
- For B: -2 to 2 → +4
- For C: -3 to 1 → +4
This suggests a horizontal translation to the right by 4 units.
Next, we'll examine the y-coordinates:
- For A: 2 to -2 → -4
- For B: 4 to -4 → -8
- For C: 0 to 0 → 0
This indicates a reflection over the x-axis (which changes the sign of the y-coordinates) followed by a downward translation by 4 units (since 2 becomes -2, and 4 becomes -4 after reflecting which requires the further downward move).
Step 3: Combine the transformations
- Reflect over the x-axis: (x, y) → (x, -y)
- Translate downward by 4 units: (x, -y) → (x, -y - 4)
Combining these gives:
- (x, y) → (x, -y) followed by (x, -y) → (x, -y - 4) results in:
- (x, y) → (x, -y - 4)
Conclusion:
The correct transformation that maps ΔA to ΔA" is: (x,y) → (x, -y - 4)
This is the second option in the provided responses.
1 answer