Use the image to answer the question.

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
A
B
C
D
first across the x
x
-axis, and then across the y
y
-axis to create square A′B′C′D′
A
′
B
′
C
′
D
′
. What are the vertices of square A′B′C′D′
A
′
B
′
C
′
D
′
?

(1 point)
Responses

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

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. Reflect square ABCD across the x-axis:

   • The original vertices are:
     • A(3, -4) → A'(3, 4)
     • B(7, -4) → B'(7, 4)
     • C(7, -8) → C'(7, 8)
     • D(3, -8) → D'(3, 8)

   After this reflection, the vertices are:

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

2. Reflect square A'B'C'D' across the y-axis:

   • Now, we apply the reflection across the y-axis which changes the x-coordinates from positive to negative:
     • A'(3, 4) → A''(-3, 4)
     • B'(7, 4) → B''(-7, 4)
     • C'(7, 8) → C''(-7, 8)
     • D'(3, 8) → D''(-3, 8)

3. Final vertices of square A''B''C''D'':

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

Therefore, the vertices of square A′B′C′D′ after both reflections 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).