Asked by Ironmarshy14
Use the image to answer the question. Identify the sequence of transformations that will carry ΔABC→ΔA"B"C" . Give your answer in the form of a composition transformation mapping. (1 point) Responses (x,y)→(x,−y−4) open paren x comma y close paren rightarrow open paren x comma negative y minus 4 close paren (x,y)→(x−4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x minus 4 comma negative y right parenthesis (x,y)→(x+4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis (x,y)→(x,−y+4) left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y plus 4 right parenthesis Skip to navigation
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Answered by
GPT-4o mini
To identify the sequence of transformations that carries ΔABC to ΔA"B"C", we need to analyze the transformations step by step based on the possible response options given:
1. **Reflection**: The transformation that involves changing the sign of the y-coordinate (if applicable) suggests a reflection across the x-axis or a vertical flip of the triangle.
2. **Translation**: The options also include translations (shifting the x or y coordinates by a certain number).
To carry out these transformations, let's use the following notation:
- A point in triangle ΔABC is represented as \( (x, y) \).
- After any transformations, the resulting points from ΔABC become ΔA"B"C".
### Step Analysis
Suppose:
1. The reflection across the x-axis would change the point \( (x, y) \) to \( (x, -y) \).
2. Then, if we move this reflected point down by 4 units, we can achieve the resulting position of \( (x, -y-4) \).
To summarize, the sequence of transformations is a reflection across the x-axis followed by a downward translation of 4 units.
### Composition Transformation Mapping
Therefore, the proper mapping that describes these transformations to carry \( ΔABC \) to \( ΔA"B"C" \) is:
\[
(x,y) \to (x, -y) \to (x, -y - 4)
\]
From the given options, the correct transformation mapping that matches this sequence is:
**(x,y)→(x,−y−4)**
This means that the point transformation from \( (x, y) \) leads to the new coordinates as \( (x, -y - 4) \), capturing both the reflection and the translation accurately.
1. **Reflection**: The transformation that involves changing the sign of the y-coordinate (if applicable) suggests a reflection across the x-axis or a vertical flip of the triangle.
2. **Translation**: The options also include translations (shifting the x or y coordinates by a certain number).
To carry out these transformations, let's use the following notation:
- A point in triangle ΔABC is represented as \( (x, y) \).
- After any transformations, the resulting points from ΔABC become ΔA"B"C".
### Step Analysis
Suppose:
1. The reflection across the x-axis would change the point \( (x, y) \) to \( (x, -y) \).
2. Then, if we move this reflected point down by 4 units, we can achieve the resulting position of \( (x, -y-4) \).
To summarize, the sequence of transformations is a reflection across the x-axis followed by a downward translation of 4 units.
### Composition Transformation Mapping
Therefore, the proper mapping that describes these transformations to carry \( ΔABC \) to \( ΔA"B"C" \) is:
\[
(x,y) \to (x, -y) \to (x, -y - 4)
\]
From the given options, the correct transformation mapping that matches this sequence is:
**(x,y)→(x,−y−4)**
This means that the point transformation from \( (x, y) \) leads to the new coordinates as \( (x, -y - 4) \), capturing both the reflection and the translation accurately.
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