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
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 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)
.
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)
.

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 across the x-axis:

   • The rule for reflecting a point \( (x, y) \) across the x-axis is \( (x, -y) \).
   • Applying this to each vertex:
     • A \( (3, -4) \) becomes A' \( (3, 4) \)
     • B \( (7, -4) \) becomes B' \( (7, 4) \)
     • C \( (7, -8) \) becomes C' \( (7, 8) \)
     • D \( (3, -8) \) becomes D' \( (3, 8) \)

2. Reflect across the y-axis:

   • The rule for reflecting a point \( (x, y) \) across the y-axis is \( (-x, y) \).
   • Applying this to the new vertices:
     • A' \( (3, 4) \) becomes A'' \( (-3, 4) \)
     • B' \( (7, 4) \) becomes B'' \( (-7, 4) \)
     • C' \( (7, 8) \) becomes C'' \( (-7, 8) \)
     • D' \( (3, 8) \) becomes D'' \( (-3, 8) \)

So, the vertices of square \( A'B'C'D' \) are:

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

The correct response is:

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