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 x-axis.
What are the coordinates of A´, B´, C´, and D´?


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

Answer 1

To reflect the square ABCD over the x-axis, we invert the y-coordinates of each point while keeping the x-coordinates the same.

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

Now reflecting each point over the x-axis:
- A' (1, -4)
- B' (4, -4)
- C' (4, -1)
- D' (1, -1)

Therefore, the coordinates after reflection are:
- A' (1, -4)
- B' (4, -4)
- C' (4, -1)
- D' (1, -1)

The correct choice that matches these coordinates is:
D: A´ (1, -4), B´ (4, -4), C´ (4, -1), and D´ (1, -1).