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 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), 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), and C′(−7,8).

Answer 1

To reflect square ABCD across the x-axis and then across the y-axis, we first need to know the original coordinates of the vertices of square ABCD.

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

Now, we'll perform the reflections:

1. **Reflection across the x-axis**: To reflect a point (x, y) across the x-axis, we change the sign of the y-coordinate. Therefore, the reflected points are:
- A'(3, -4)
- B'(7, -4)
- C'(7, -8)
- D'(3, -8)

2. **Reflection across the y-axis**: To reflect a point (x, y) across the y-axis, we change the sign of the x-coordinate. Applying this to the points we just calculated:
- A''(-3, -4)
- B''(-7, -4)
- C''(-7, -8)
- D''(-3, -8)

Now square A'B'C'D' has the following vertices:
- A'(-3, -4)
- B'(-7, -4)
- C'(-7, -8)
- D'(-3, -8)

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