Question

Reflect square ABCD first across the x -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)
Responses

Square A′B′C′D′ has vertices A′(3,4), B′(7,4), C′(7,8), and D′(3,8).
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis 3 comma 4 right parenthesis , upper B prime left parenthesis 7 comma 4 right parenthesis , upper C prime left parenthesis 7 comma 8 right parenthesis , and upper D prime left parenthesis 3 comma 8 right parenthesis .

Square A′B′C′D′ has vertices A′(−3,4), B′(−7,4), C′(−7,8), and D′(−3,8).
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 3 comma 4 right parenthesis , upper B prime left parenthesis negative 7 comma 4 right parenthesis , upper C prime left parenthesis negative 7 comma 8 right parenthesis , and upper D prime left parenthesis negative 3 comma 8 right parenthesis .

Square A′B′C′D′ has vertices A′(−3,−4), B′(−7,−4), C′(−7,−8), and D′(−3,−8).
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 3 comma negative 4 right parenthesis , upper B prime left parenthesis negative 7 comma negative 4 right parenthesis , upper C prime left parenthesis negative 7 comma negative 8 right parenthesis , and upper D prime left parenthesis negative 3 comma negative 8 right parenthesis .

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

Answer 1

To determine the vertices of square A'B'C'D' after reflecting square ABCD first across the x-axis and then across the y-axis, we need to perform the reflections step-by-step.

### Step 1: Reflect Across the x-axis

When a point (x, y) is reflected across the x-axis, its new coordinates become (x, -y).

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

After reflecting across the x-axis, when we reflect across the y-axis, the coordinates change from (x, -y) to (-x, -y).

### Applying the Reflections

Let's assume the vertices of square ABCD are:
- A(3, 4)
- B(7, 4)
- C(7, 8)
- D(3, 8)

**1. Reflecting across the x-axis:**
- A(3, 4) → A'(3, -4)
- B(7, 4) → B'(7, -4)
- C(7, 8) → C'(7, -8)
- D(3, 8) → D'(3, -8)

**2. Reflecting across the y-axis:**
- A'(3, -4) → A''(-3, -4)
- B'(7, -4) → B''(-7, -4)
- C'(7, -8) → C''(-7, -8)
- D'(3, -8) → D''(-3, -8)

### Vertices of A′B′C′D′

After performing both reflections, the coordinates of square A′B′C′D′ are:
- A''(-3, -4)
- B''(-7, -4)
- C''(-7, -8)
- D''(-3, -8)

Thus, the correct response is:
**Square A′B′C′D′ has vertices A′(−3,−4), B′(−7,−4), C′(−7,−8), and D′(−3,−8).**