Question
Describe in words how to map Upper DeltaEFG to its image Upper DeltaE'F'G'. Use pencil and paper. Graph another reflection of Upper DeltaEFG.
-6
0
-6
6
x
y
E
F
G
E'
F'
G'
A horizontal x-axis is labeled from negative 6 to 0. A vertical y-axis is labeled from negative 6 to 6. There are two triangles plotted. Triangle E F G has the following vertices: E, (negative 3, 4); F, (negative 2, 4); G, (negative 5, 2). Triangle E prime F prime G prime has the following vertices: E prime, (negative 3, negative 4); F prime, (negative 2, negative 4); G prime, (negative 5, negative 2).
Question content area bottom
Part 1
Which words below describe the mapping?
A.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the x-axis.
B.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the line yequals2.
C.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the y-axis.
D.
Upper DeltaE'F'G' is the image of Upper DeltaEFG translated 2 units vertically.
-6
0
-6
6
x
y
E
F
G
E'
F'
G'
A horizontal x-axis is labeled from negative 6 to 0. A vertical y-axis is labeled from negative 6 to 6. There are two triangles plotted. Triangle E F G has the following vertices: E, (negative 3, 4); F, (negative 2, 4); G, (negative 5, 2). Triangle E prime F prime G prime has the following vertices: E prime, (negative 3, negative 4); F prime, (negative 2, negative 4); G prime, (negative 5, negative 2).
Question content area bottom
Part 1
Which words below describe the mapping?
A.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the x-axis.
B.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the line yequals2.
C.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the y-axis.
D.
Upper DeltaE'F'G' is the image of Upper DeltaEFG translated 2 units vertically.
Answers
GPT-4o mini
To map Upper Delta \( EFG \) to its image Upper Delta \( E'F'G' \), we first identify the key coordinates of the vertices involved.
1. **Vertices of Upper Delta \( EFG \)**:
- \( E = (-3, 4) \)
- \( F = (-2, 4) \)
- \( G = (-5, 2) \)
2. **Vertices of Upper Delta \( E'F'G' \)**:
- \( E' = (-3, -4) \)
- \( F' = (-2, -4) \)
- \( G' = (-5, -2) \)
### Mapping Description
The transformation that has occurred to map Triangle \( EFG \) to Triangle \( E'F'G' \) involves a reflection.
- To understand how the reflection is performed, let's look closely at the \( y \)-coordinates of the vertices:
- The \( y \)-coordinate of \( E \) is \( 4 \), and the \( y \)-coordinate of \( E' \) is \( -4 \). This shows that point \( E \) was reflected across the x-axis.
- For point \( F \): The \( y \)-coordinate changed from \( 4 \) to \( -4 \).
- For point \( G \): The \( y \)-coordinate changed from \( 2 \) to \( -2 \).
In each case, the \( y \)-coordinate of each vertex of Triangle \( EFG \) becomes the negative of its original value when mapped to Triangle \( E'F'G' \). This indicates that Triangle \( E'F'G' \) is indeed the reflection of Triangle \( EFG \) across the x-axis.
### Conclusion on Mapping
With that observation, the words that describe the mapping between Upper Delta \( EFG \) to Upper Delta \( E'F'G' \) is:
**A. Upper Delta \( E'F'G' \) is the image of Upper Delta \( EFG \) after a reflection across the \( x \)-axis.**
### Reflection of Upper Delta \( EFG \)
If you'd like to graph another reflection, you can reflect Upper Delta \( EFG \) across a different line, such as the \( y \)-axis.
#### Reflecting across the y-axis:
- For the reflection across the \( y \)-axis, you will change the \( x \)-coordinates of each vertex as follows:
1. Vertex \( E (-3, 4) \) becomes \( E'' (3, 4) \).
2. Vertex \( F (-2, 4) \) becomes \( F'' (2, 4) \).
3. Vertex \( G (-5, 2) \) becomes \( G'' (5, 2) \).
Now, you would plot the points \( E'' (3, 4) \), \( F'' (2, 4) \), and \( G'' (5, 2) \) to create a new triangle that is the reflection of \( EFG \) across the \( y \)-axis.
1. **Vertices of Upper Delta \( EFG \)**:
- \( E = (-3, 4) \)
- \( F = (-2, 4) \)
- \( G = (-5, 2) \)
2. **Vertices of Upper Delta \( E'F'G' \)**:
- \( E' = (-3, -4) \)
- \( F' = (-2, -4) \)
- \( G' = (-5, -2) \)
### Mapping Description
The transformation that has occurred to map Triangle \( EFG \) to Triangle \( E'F'G' \) involves a reflection.
- To understand how the reflection is performed, let's look closely at the \( y \)-coordinates of the vertices:
- The \( y \)-coordinate of \( E \) is \( 4 \), and the \( y \)-coordinate of \( E' \) is \( -4 \). This shows that point \( E \) was reflected across the x-axis.
- For point \( F \): The \( y \)-coordinate changed from \( 4 \) to \( -4 \).
- For point \( G \): The \( y \)-coordinate changed from \( 2 \) to \( -2 \).
In each case, the \( y \)-coordinate of each vertex of Triangle \( EFG \) becomes the negative of its original value when mapped to Triangle \( E'F'G' \). This indicates that Triangle \( E'F'G' \) is indeed the reflection of Triangle \( EFG \) across the x-axis.
### Conclusion on Mapping
With that observation, the words that describe the mapping between Upper Delta \( EFG \) to Upper Delta \( E'F'G' \) is:
**A. Upper Delta \( E'F'G' \) is the image of Upper Delta \( EFG \) after a reflection across the \( x \)-axis.**
### Reflection of Upper Delta \( EFG \)
If you'd like to graph another reflection, you can reflect Upper Delta \( EFG \) across a different line, such as the \( y \)-axis.
#### Reflecting across the y-axis:
- For the reflection across the \( y \)-axis, you will change the \( x \)-coordinates of each vertex as follows:
1. Vertex \( E (-3, 4) \) becomes \( E'' (3, 4) \).
2. Vertex \( F (-2, 4) \) becomes \( F'' (2, 4) \).
3. Vertex \( G (-5, 2) \) becomes \( G'' (5, 2) \).
Now, you would plot the points \( E'' (3, 4) \), \( F'' (2, 4) \), and \( G'' (5, 2) \) to create a new triangle that is the reflection of \( EFG \) across the \( y \)-axis.