A(-2, 4) and B(-4, 2) are reflected in the y-axis. If A and B' are images of A and B respectively.
State whether AB' = BA'

Answer

To solve the problem, we will follow these steps:

1. **Identify the coordinates of points A and B:**
- Point A is given as A(-2, 4).
- Point B is given as B(-4, 2).

2. **Reflect points A and B in the y-axis:**
- When a point (x, y) is reflected in the y-axis, its image becomes (-x, y).
- For point A(-2, 4), the reflection A' will be:
\[ A' = (2, 4) \]
- For point B(-4, 2), the reflection B' will be:
\[ B' = (4, 2) \]

3. **Calculate the distance AB':**
- We will use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, A(-2, 4) and B'(4, 2):
\[ AB' = \sqrt{(4 - (-2))^2 + (2 - 4)^2} \]
\[ = \sqrt{(4 + 2)^2 + (2 - 4)^2} \]
\[ = \sqrt{(6)^2 + (-2)^2} \]
\[ = \sqrt{36 + 4} \]
\[ = \sqrt{40} \]

4. **Calculate the distance BA':**
- Now, we will calculate the distance from B(-4, 2) to A'(2, 4):
\[ BA' = \sqrt{(2 - (-4))^2 + (4 - 2)^2} \]
\[ = \sqrt{(2 + 4)^2 + (4 - 2)^2} \]
\[ = \sqrt{(6)^2 + (2)^2} \]
\[ = \sqrt{36 + 4} \]
\[ = \sqrt{40} \]

5. **Compare the distances AB' and BA':**
- We found that:
\[ AB' = \sqrt{40} \]
\[ BA' = \sqrt{40} \]
- Therefore, we can conclude:
\[ AB' = BA' \]

### Final Conclusion:
Yes, \( AB' = BA' \).