Exercise 3: Reflection in the y-axis.
Exercise 4: Neither axis.
Exercise 5: Neither axis.
Exercise 6: Reflection in the y-axis.
We can analyze the coordinate changes between the original triangle (ABC) and its reflection (EDF) to determine the type of reflection (x-axis, y-axis, or neither) occurring in each exercise:
1. Analyze coordinate changes:
- Reflection in the x-axis: The y-coordinate changes sign (flips) while the x-coordinate remains the same.
- Reflection in the y-axis: The x-coordinate changes sign (flips) while the y-coordinate remains the same.
- Neither: If neither coordinate changes sign, or both change together, it's not a reflection in either axis.
2. Apply the analysis to each exercise:
Exercise 3:
- A(-2, -1) to E(1, -1): x-coordinate flips, confirming reflection in the y-axis.
- B(-1, -1) to D(2, -1): x-coordinate flips, confirming reflection in the y-axis.
- C(-2, -5) to F(2, -5): x-coordinate flips, confirming reflection in the y-axis.
Exercise 4:
- A(-2, 0) to E(2, -1): Both coordinates change, suggesting neither axis.
- B(-1, 2) to D(1, 0): Both coordinates change, confirming neither axis.
- C(-2, -5) to F(1, -5): x-coordinate flips, y-coordinate changes, contradicting previous observations.
Exercise 5:
- A(4, 1) to E(-1, -1): Both coordinates change, suggesting neither axis.
- B(1, 1) to D(-1, -1): Both coordinates change, confirming neither axis.
- C(3, 4) to F(-4, -3): Both coordinates change significantly, confirming neither axis.
Exercise 6:
- A(2, 1) to E(2, -3): y-coordinate flips, confirming reflection in the y-axis.
- B(2, 3) to D(2, -1): y-coordinate flips, confirming reflection in the y-axis.
- C(6, 1) to F(6, -1): y-coordinate flips, confirming reflection in the y-axis.
The summary is :
- Exercise 3: Reflection in the y-axis.
- Exercise 4: Neither axis.
- Exercise 5: Neither axis.
- Exercise 6: Reflection in the y-axis.
By analyzing the coordinate changes, we can determine the type of reflection occurring in each exercise. Remember, if both coordinates change sign together or neither changes, it's not a reflection in either axis.