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)
, 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)
.
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 .
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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. **Initial vertices of square ABCD:**
- \(A(3, -4)\)
- \(B(7, -4)\)
- \(C(7, -8)\)
- \(D(3, -8)\)

2. **Reflect across the x-axis:**
- When reflecting a point \((x, y)\) across the x-axis, the new coordinates become \((x, -y)\).
- Thus, the new vertices after reflecting across the x-axis are:
- \(A'(3, 4)\)
- \(B'(7, 4)\)
- \(C'(7, 8)\)
- \(D'(3, 8)\)

3. **Reflect across the y-axis:**
- When reflecting a point \((x, y)\) across the y-axis, the new coordinates become \((-x, y)\).
- Thus, the new vertices after reflecting across the y-axis are:
- \(A''(-3, 4)\)
- \(B''(-7, 4)\)
- \(C''(-7, 8)\)
- \(D''(-3, 8)\)

Combining these results, the final vertices of square \(A'B'C'D'\) after both reflections are:
- \(A'(-3, 4)\)
- \(B'(-7, 4)\)
- \(C'(-7, 8)\)
- \(D'(-3, 8)\)

The correct response from the options provided is:

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