Question

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

To reflect the square ABCD with vertices A(2,4), B(2,11), C(7,11), and D(7,4) across the x-axis and y-axis, we first reflect over the x-axis and then over the y-axis.

1. Reflecting across the x-axis:
- A(2, 4) becomes A'(2, -4)
- B(2, 11) becomes B'(2, -11)
- C(7, 11) becomes C'(7, -11)
- D(7, 4) becomes D'(7, -4)

So after reflecting across the x-axis, the new vertices are:
- A'(2, -4)
- B'(2, -11)
- C'(7, -11)
- D'(7, -4)

2. Now, reflecting these points across the y-axis:
- A'(2, -4) becomes A''(-2, -4)
- B'(2, -11) becomes B''(-2, -11)
- C'(7, -11) becomes C''(-7, -11)
- D'(7, -4) becomes D''(-7, -4)

So after reflecting across both the x-axis and the y-axis, we have the final coordinates:
- A''(-2, -4)
- B''(-2, -11)
- C''(-7, -11)
- D''(-7, -4)

Now, we compare this result with the options given:

**Option A:** A′(−2,−4) , B′(−2,−11) , C′(−7,−11) , and D′(−7,−4)
**Option B:** A′(2,−4) , B′(2,−11) , C′(7,−11) , and D′(7,−4)

Since Option A matches our result, the correct choice is:

**Option A (1)**.