Question
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), 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 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), and C′(−7,8).
Answers
Answered by
GPT-4o mini
To reflect a square first across the x-axis and then across the y-axis, we can follow these steps:
1. **Initial Coordinates of Square ABCD**: Assume the initial coordinates of square ABCD are A(3, 4), B(7, 4), C(7, 8), and D(3, 8).
2. **Reflect Across the X-Axis**:
- When reflecting across the x-axis, the y-coordinates change signs while the x-coordinates remain the same.
- After reflecting:
- A' = (3, -4)
- B' = (7, -4)
- C' = (7, -8)
- D' = (3, -8)
3. **Reflect Across the Y-Axis**:
- When reflecting across the y-axis, the x-coordinates change signs while the y-coordinates remain the same.
- After reflecting:
- A'' = (-3, -4)
- B'' = (-7, -4)
- C'' = (-7, -8)
- D'' = (-3, -8)
Thus, the 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 is: Square A′B′C′D′ has vertices A′(−3,−4), B′(−7,−4), C′(−7,−8), and D′(−3,−8).
1. **Initial Coordinates of Square ABCD**: Assume the initial coordinates of square ABCD are A(3, 4), B(7, 4), C(7, 8), and D(3, 8).
2. **Reflect Across the X-Axis**:
- When reflecting across the x-axis, the y-coordinates change signs while the x-coordinates remain the same.
- After reflecting:
- A' = (3, -4)
- B' = (7, -4)
- C' = (7, -8)
- D' = (3, -8)
3. **Reflect Across the Y-Axis**:
- When reflecting across the y-axis, the x-coordinates change signs while the y-coordinates remain the same.
- After reflecting:
- A'' = (-3, -4)
- B'' = (-7, -4)
- C'' = (-7, -8)
- D'' = (-3, -8)
Thus, the 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 is: Square A′B′C′D′ has vertices A′(−3,−4), B′(−7,−4), C′(−7,−8), and D′(−3,−8).