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, 5); F, (negative 2, 2); G, (negative 4, 2). Triangle E prime F prime G prime has the following vertices: E prime, (negative 3, negative 5); F prime, (negative 2, negative 2); G prime, (negative 4, 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 line yequals2.
B.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the y-axis.
C.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the x-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, 5); F, (negative 2, 2); G, (negative 4, 2). Triangle E prime F prime G prime has the following vertices: E prime, (negative 3, negative 5); F prime, (negative 2, negative 2); G prime, (negative 4, 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 line yequals2.
B.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the y-axis.
C.
Upper DeltaE'F'G' is the image of Upper DeltaEFG after a reflection across the x-axis.
D.
Upper DeltaE'F'G' is the image of Upper DeltaEFG translated 2 units vertically.
Answers
GPT-4o mini
To describe the mapping of Upper Delta EFG to its image Upper Delta E'F'G', we analyze the coordinates of the corresponding points before and after the transformation:
1. **Original Triangle EFG Vertices:**
- E (−3, 5)
- F (−2, 2)
- G (−4, 2)
2. **Reflected Triangle E'F'G' Vertices:**
- E' (−3, −5)
- F' (−2, −2)
- G' (−4, −2)
**Mapping Analysis:**
- In comparing the original coordinates of triangle EFG with the transformed coordinates of triangle E'F'G':
- The x-coordinates remain the same: -3, -2, and -4.
- The y-coordinates are negated (reflected): 5 becomes -5, 2 becomes -2.
This indicates that the transformation involved taking each point and reflecting it across the x-axis, where the y-coordinate of each point is changed to its negative.
**Conclusion for Part 1:**
The correct description of the mapping is:
**C. Upper Delta E'F'G' is the image of Upper Delta EFG after a reflection across the x-axis.**
---
**Part 2: Reflection of Upper Delta EFG:**
To graph another reflection of Upper Delta EFG, we could reflect it across the y-axis as an example:
1. **Reflecting across the y-axis:**
- E (−3, 5) becomes E'' (3, 5)
- F (−2, 2) becomes F'' (2, 2)
- G (−4, 2) becomes G'' (4, 2)
2. **Vertices of the New Triangle E''F''G'':**
- E'' (3, 5)
- F'' (2, 2)
- G'' (4, 2)
Now, you can plot Triangle E''F''G'' on the coordinate system, and it would show the reflection of Upper Delta EFG across the y-axis. The new triangle vertices would be located in the first quadrant of the graph, reflecting the same shape of the original triangle but in a different position.
1. **Original Triangle EFG Vertices:**
- E (−3, 5)
- F (−2, 2)
- G (−4, 2)
2. **Reflected Triangle E'F'G' Vertices:**
- E' (−3, −5)
- F' (−2, −2)
- G' (−4, −2)
**Mapping Analysis:**
- In comparing the original coordinates of triangle EFG with the transformed coordinates of triangle E'F'G':
- The x-coordinates remain the same: -3, -2, and -4.
- The y-coordinates are negated (reflected): 5 becomes -5, 2 becomes -2.
This indicates that the transformation involved taking each point and reflecting it across the x-axis, where the y-coordinate of each point is changed to its negative.
**Conclusion for Part 1:**
The correct description of the mapping is:
**C. Upper Delta E'F'G' is the image of Upper Delta EFG after a reflection across the x-axis.**
---
**Part 2: Reflection of Upper Delta EFG:**
To graph another reflection of Upper Delta EFG, we could reflect it across the y-axis as an example:
1. **Reflecting across the y-axis:**
- E (−3, 5) becomes E'' (3, 5)
- F (−2, 2) becomes F'' (2, 2)
- G (−4, 2) becomes G'' (4, 2)
2. **Vertices of the New Triangle E''F''G'':**
- E'' (3, 5)
- F'' (2, 2)
- G'' (4, 2)
Now, you can plot Triangle E''F''G'' on the coordinate system, and it would show the reflection of Upper Delta EFG across the y-axis. The new triangle vertices would be located in the first quadrant of the graph, reflecting the same shape of the original triangle but in a different position.