Question

How many of the following statements hold true when a square is reflected about the line $y=x$ in the coordinate plane?
1. The shape of the square changes.
2. The size of the square changes.
3. The coordinates of its vertices changes.
4. The length of its diagonals remains the same.
5. The angular measures of the image and the preimage are the same.
6. The perimeter of the square changes.

• A. 6
• B. 5
• C. 1
• D. 3

Answer 1

The correct option is D 3

We know that after any rigid transformation (reflection, rotation, or translation), the preimage and the image have the same side lengths, diagonal lengths, angle measures, perimeter, and area, but different positions.
Hence,
statement 1 is not true as the shape of the figure doesn’t change after rigid transformations,
statement 2 is not true as the shape of the figure doesn’t change after rigid transformations,
statement 3 is true as the position of the figure changes after rigid transformations which in turn changes the coordinates of the vertices,
statement 4 is true as the length of the diagonal remains the same after rigid transformations,
statement 5 is true as the angular measures remain the same after rigid transformations, and
statement 6 is not true as the perimeter of the figure doesn’t change after the rigid transformations.
Hence, 3 statements are true.
$\to$ Option B is correct.