Question

The given line segment AB is reflected across the $y$-axis to get the line segment A'B'.

Which of the following statements is not true?

• A. Length of AB = Length of A'B'
• B. None of the above
• C. B and B' have the same $x$-coordinate.
• D. B and B' have the same $y$-coordinate.

Answer 1

The correct option is C B and B' have the same $x$-coordinate.

Given: Line segment AB is reflected across the $y$-axis to get line segment A'B'.
We know that after any transformation (reflection, rotation, or translation), the preimage and the image have the same side lengths, angle measures, perimeter, and area, but different positions.
So, the length of AB = length of A'B'.
Hence, option A is true.
The image shown below demonstrates the reflection of the line segment AB across the $y$-axis to get the line segment A'B'

We can observe that the coordinates of point B are (3, 5) and the coordinates of point B' are (-3, 5). So, we can say that points B and B' have the same $y$-coordinate, but different $x$-coordinate. $\to$ Option B is correct.