Question

Question
Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 9 to 9 in one unit increments. The y-axis ranges from negative 11 to 11 in one unit increments. Four points are plotted. A square is graphed using the four plotted points as vertices. Point A is plotted at coordinates left parenthesis 3 comma negative 4 right parenthesis. Point B is plotted at coordinates left parenthesis 7 comma negative 4 right parenthesis. Point C is plotted at coordinates left parenthesis 7 comma negative 8 right parenthesis. Point D is plotted at coordinates left parenthesis 3 comma negative 8 right parenthesis. Points A, B, C, and D are connected by solid lines to form square A B C D.

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 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 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)
, and C′(−7,8)
.
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 , and upper C prime left parenthesis negative 7 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 .
Skip to navigation

Answer 1

To find the vertices of square A′B′C′D′ after reflecting square ABCD first across the x-axis and then across the y-axis, we can follow these steps:

1. **Original Vertices**:
- A(3, -4)
- B(7, -4)
- C(7, -8)
- D(3, -8)

2. **Reflecting across the x-axis**:
- The rule for reflection across the x-axis is (x, y) becomes (x, -y).
- Therefore, the points after the first reflection are:
- A'(3, 4)
- B'(7, 4)
- C'(7, 8)
- D'(3, 8)

3. **Reflecting across the y-axis**:
- The rule for reflection across the y-axis is (x, y) becomes (-x, y).
- Therefore, the points after the second reflection are:
- A′(−3, 4)
- B′(−7, 4)
- C′(−7, 8)
- D′(−3, 8)

Thus, the vertices of square A′B′C′D′ are:
- A′(−3, 4)
- B′(−7, 4)
- C′(−7, 8)
- D′(−3, 8)

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