Question

A square ABCD has the following coordinates:
A (1, 4), B (4, 4), C (4, 1), and D (1, 1).
It is reflected over the y-axis.
What are the coordinates of A´, B´, C´ and D´?


Choose the best answer from the options below:
A A´(1,-4 ) , B´(4,-4), C´(4.-1), and D´(1,-1)
B A´( -4,1), B´(4,-4), C´( -1,4), and D´(1,-1)
C A´(-1,4), B´(-4,4), C´( -4,1), and D´(-1,1)
D None of these

Answer 1

To find the coordinates of the square ABCD after it is reflected over the y-axis, we need to change the x-coordinates of each point to their opposite values (i.e., multiply them by -1) while keeping the y-coordinates the same.

The original coordinates of the vertices are:
- A(1, 4)
- B(4, 4)
- C(4, 1)
- D(1, 1)

After reflecting over the y-axis, the new coordinates will be:
- A'(-1, 4)
- B'(-4, 4)
- C'(-4, 1)
- D'(-1, 1)

Now let's check the options given:

A. A´(1,-4), B´(4,-4), C´(4,-1), and D´(1,-1) - **Incorrect**
B. A´(-4,1), B´(4,-4), C´(-1,4), and D´(1,-1) - **Incorrect**
C. A´(-1,4), B´(-4,4), C´(-4,1), and D´(-1,1) - **Partially correct; A' and D' are correct, but B' and C' are not correct**
D. None of these - **Correct**

Therefore, the best answer is **D: None of these.**