Question

Reflect square ABCD first across the z-axis, and then across the y-axis to create square A' * B' * C' * D' What are the vertices of square A' * B' * C' * D'

(1 point)

Square A' * B' * C' * D' has vertices A' (3, 4), B' * (7, 4) C' (7, 8), and D' (3,8).

Square A' * B' * C' * D' has vertices A' * (- 3, - 4) B' * (- 7, - 4) C' * (- 7, - 8) and D' * (- 3, - 8)

Square A' * B' * C' * D' has vertices A' * (- 3, 4) B' * (- 7, 4) C' * (- 7, 8) and D' * (- 3, 8)

Square A' * B' * C' * D' has vertices A' * (- 3, 4) B' * (- 7, 4) and C' * (- 7, 8)

Starting points for the square
A: 3, -4
B: 7, -4
C: 7, -8
D: 3, -8

Answer 1

To find the vertices of square A'B'C'D' after performing the reflections, we'll start with the original vertices A, B, C, and D:

- A(3, -4)
- B(7, -4)
- C(7, -8)
- D(3, -8)

### Step 1: Reflect across the z-axis

Since the square lies in the xy-plane, reflecting across the z-axis does not change the x and y coordinates. Thus, after reflecting across the z-axis, the vertices remain the same:

- A(3, -4) → A'(3, -4)
- B(7, -4) → B'(7, -4)
- C(7, -8) → C'(7, -8)
- D(3, -8) → D'(3, -8)

### Step 2: Reflect across the y-axis

When reflecting across the y-axis, the x-coordinates are negated while y-coordinates stay the same. Applying this reflection to the vertices A', B', C', and D':

- A'(3, -4) → A''(-3, -4)
- B'(7, -4) → B''(-7, -4)
- C'(7, -8) → C''(-7, -8)
- D'(3, -8) → D''(-3, -8)

### Final Result

The new vertices of the square A''B''C''D'' after both reflections are:

- A''(-3, -4)
- B''(-7, -4)
- C''(-7, -8)
- D''(-3, -8)

So, the correct option is:

**Square A' * B' * C' * D' has vertices A' * (-3, -4), B' * (-7, -4), C' * (-7, -8), and D' * (-3, -8)**.