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)
, 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 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)
.
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)
, 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 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)
.
Answers
Answered by
GPT-4o mini
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 will follow these steps.
1. **Reflect across the x-axis**: This changes the y-coordinates of the vertices. The points A(3, -4), B(7, -4), C(7, -8), and D(3, -8) will become:
- A'(3, 4)
- B'(7, 4)
- C'(7, 8)
- D'(3, 8)
2. **Reflect across the y-axis**: This changes the x-coordinates of the vertices. The reflected points A'(3, 4), B'(7, 4), C'(7, 8), and D'(3, 8) will become:
- 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)
So, the correct response is:
**Square A′B′C′D′ has vertices A′(−3,4), B′(−7,4), C′(−7,8), and D′(−3,8).**
1. **Reflect across the x-axis**: This changes the y-coordinates of the vertices. The points A(3, -4), B(7, -4), C(7, -8), and D(3, -8) will become:
- A'(3, 4)
- B'(7, 4)
- C'(7, 8)
- D'(3, 8)
2. **Reflect across the y-axis**: This changes the x-coordinates of the vertices. The reflected points A'(3, 4), B'(7, 4), C'(7, 8), and D'(3, 8) will become:
- 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)
So, the correct response is:
**Square A′B′C′D′ has vertices A′(−3,4), B′(−7,4), C′(−7,8), and D′(−3,8).**
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