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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) , 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 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) .
Answers
Answered by
GPT-4o mini
To determine the vertices of square A′B′C′D′ after reflecting square ABCD first across the x-axis and then across the y-axis, let's consider the process step by step.
Assuming that the vertices of square ABCD are as follows:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
- D(x₄, y₄)
### Step 1: Reflect across the x-axis
When reflecting a point (x, y) across the x-axis, the new coordinates become (x, -y).
Thus, the vertices after reflecting across the x-axis will be:
- A′(x₁, -y₁)
- B′(x₂, -y₂)
- C′(x₃, -y₃)
- D′(x₄, -y₄)
### Step 2: Reflect across the y-axis
Next, we reflect the result across the y-axis. When reflecting a point (x, y) across the y-axis, the new coordinates become (-x, y).
Therefore, the vertices after reflecting across the y-axis will become:
- A′′(−x₁, -y₁)
- B′′(−x₂, -y₂)
- C′′(−x₃, -y₃)
- D′′(−x₄, -y₄)
Now, let's identify the original coordinates for square ABCD.
Assume the original square ABCD has the following coordinates:
- A(3, 4)
- B(7, 4)
- C(7, 8)
- D(3, 8)
### Apply Step 1 (reflection across the x-axis):
- A′(3, -4)
- B′(7, -4)
- C′(7, -8)
- D′(3, -8)
### Apply Step 2 (reflection across the y-axis):
- 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), and D′(−3, −8).
Hence, the correct response is:
Square A′B′C′D′ has vertices A′(−3, −4), B′(−7, −4), C′(−7, −8), and D′(−3, −8).
Assuming that the vertices of square ABCD are as follows:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
- D(x₄, y₄)
### Step 1: Reflect across the x-axis
When reflecting a point (x, y) across the x-axis, the new coordinates become (x, -y).
Thus, the vertices after reflecting across the x-axis will be:
- A′(x₁, -y₁)
- B′(x₂, -y₂)
- C′(x₃, -y₃)
- D′(x₄, -y₄)
### Step 2: Reflect across the y-axis
Next, we reflect the result across the y-axis. When reflecting a point (x, y) across the y-axis, the new coordinates become (-x, y).
Therefore, the vertices after reflecting across the y-axis will become:
- A′′(−x₁, -y₁)
- B′′(−x₂, -y₂)
- C′′(−x₃, -y₃)
- D′′(−x₄, -y₄)
Now, let's identify the original coordinates for square ABCD.
Assume the original square ABCD has the following coordinates:
- A(3, 4)
- B(7, 4)
- C(7, 8)
- D(3, 8)
### Apply Step 1 (reflection across the x-axis):
- A′(3, -4)
- B′(7, -4)
- C′(7, -8)
- D′(3, -8)
### Apply Step 2 (reflection across the y-axis):
- 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), and D′(−3, −8).
Hence, the correct response is:
Square A′B′C′D′ has vertices A′(−3, −4), B′(−7, −4), C′(−7, −8), and D′(−3, −8).