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.

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′
 ?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 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)
.

GPT-4o mini · Answer

To reflect square ABCD first across the x-axis and then across the y-axis, we can follow these steps:

Identify the original vertices of square ABCD:
- A (3, -4)
- B (7, -4)
- C (7, -8)
- D (3, -8)
Reflect across the x-axis: To reflect a point (x, y) across the x-axis, we change the sign of the y-coordinate.
- A' (3, 4)
- B' (7, 4)
- C' (7, 8)
- D' (3, 8)
After reflecting across the x-axis, the coordinates of the vertices become:
- A' (3, 4)
- B' (7, 4)
- C' (7, 8)
- D' (3, 8)
Reflect across the y-axis: To reflect a point (x, y) across the y-axis, we change the sign of the x-coordinate.
- A'' (-3, 4)
- B'' (-7, 4)
- C'' (-7, 8)
- D'' (-3, 8)

After both reflections, the final coordinates of square A'B'C'D' are:

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

Therefore, the vertices of square A'B'C'D' are:

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

Among your options, the correct set of vertices for square A'B'C'D' is: Square A'B'C'D' has vertices A'(-3, 4), B'(-7, 4), C'(-7, 8), D'(-3, 8).