Question

Square ABCD has vertices A(2,4) , B(2,11) , C(7,11) , and D(7,4) . The square ABCD is reflected on the x -axis and the y -axis. Find the coordinates of the vertices for square A′B′C′D′ . Choose 1 for Option A and 2 for Option B. Option A: Square A′B′C′D′ has vertices A′(−2,−4) , B′(−2,−11) , C′(−7,−11) , and D′(−7,−4) . Option B: Square A′B′C′D′ has vertices A′(2,−4) , B′(2,−11) , C′(7,−11) , and D′(7,−4) .(1 point)

Answer 1

After reflecting square ABCD on both the x-axis and y-axis, the vertices of square A'B'C'D' will have coordinates A'(−2,−4), B'(−2,−11), C'(−7,−11), and D'(−7,−4), which corresponds to Option A.

To find the coordinates of the vertices for square (A'B'C'D') after reflecting square (ABCD) over the x-axis and the y-axis:

For x-axis reflection, the y-coordinate is negated, and for y-axis reflection, the x-coordinate is negated.

1. X-axis reflection:

`- A'(\(2, -4\))`

`- B'(\(2, -11\))`

`- C'(\(7, -11\))`

`- D'(\(7, -4\))`

2. Y-axis reflection:

`- A'(\(-2, 4\))`

`- B'(\(-2, 11\))`

`- C'(\(-7, 11\))`

`- D'(\(-7, 4\))`

Comparing these results with the given options:

- Option A matches the coordinates after both reflections.

- Option B does not match the coordinates after the y-axis reflection.

Therefore, the correct answer is Option A: Square
`\(A'B'C'D'\)` has vertices
`A'(\(-2, -4\))`,
`B'(\(-2, -11\))`,
`C'(\(-7, -11\))`, and
`D'(\(-7, -4\))`.