Question
Use the image to determine the type of transformation shown.
image of polygon ABCD with A at negative 4 comma negative 1, B at negative 2 comma negative 2, C at negative 2 comma negative 5 and D at negative 7 comma negative 5 and a second polygon A prime B prime C prime D prime with A prime at negative 1 comma 4, B prime at negative 2 comma 2, C prime at negative 5 comma 2, and D prime at negative 5 comma 7
90° counterclockwise rotation
90° clockwise rotation
Reflection across the y-axis
Horizontal translation
image of polygon ABCD with A at negative 4 comma negative 1, B at negative 2 comma negative 2, C at negative 2 comma negative 5 and D at negative 7 comma negative 5 and a second polygon A prime B prime C prime D prime with A prime at negative 1 comma 4, B prime at negative 2 comma 2, C prime at negative 5 comma 2, and D prime at negative 5 comma 7
90° counterclockwise rotation
90° clockwise rotation
Reflection across the y-axis
Horizontal translation
Answers
Answered by
GPT-4o mini
To determine the type of transformation that maps polygon ABCD to polygon A'B'C'D', we need to analyze the coordinates of the points in both polygons.
For polygon ABCD:
- A: (-4, -1)
- B: (-2, -2)
- C: (-2, -5)
- D: (-7, -5)
For polygon A'B'C'D':
- A': (-1, 4)
- B': (-2, 2)
- C': (-5, 2)
- D': (-5, 7)
### Analyzing the points:
1. **A to A'**:
- A: (-4, -1) → A': (-1, 4)
- The x-coordinate changed from -4 to -1 (+3), and the y-coordinate changed from -1 to 4 (+5).
2. **B to B'**:
- B: (-2, -2) → B': (-2, 2)
- The x-coordinate remains the same, but the y-coordinate changed from -2 to 2 (+4).
3. **C to C'**:
- C: (-2, -5) → C': (-5, 2)
- The x-coordinate changed from -2 to -5 (-3), and the y-coordinate changed from -5 to 2 (+7).
4. **D to D'**:
- D: (-7, -5) → D': (-5, 7)
- The x-coordinate changed from -7 to -5 (+2), and the y-coordinate changed from -5 to 7 (+12).
### Looking for patterns:
- The changes in the coordinates suggest a combination of translation and possibly rotation, primarily because the coordinates of A and D change significantly.
### Rotation:
To check if it could be a 90° rotation, let's apply a 90° counterclockwise rotation to the original coordinates.
The rule for a 90° counterclockwise rotation is:
- (x, y) → (-y, x).
Let's rotate point A (-4, -1):
- A' = (1, -4) -- which does not match.
Continuing this for others doesn't give matching after rotation.
### Reflection:
If we reflect across the y-axis:
- (x, y) → (-x, y)
Rotating and reflecting didn't match up either as seen from analyses.
### Conclusion:
In context to made observations, the coordinates show more sign of translation rather than a clear reflection or rotation, so the transformation appears to be a **horizontal translation** (as others would not fit).
Therefore, the correct match of transformation for ABCD to A'B'C'D' is the **Horizontal translation.**
For polygon ABCD:
- A: (-4, -1)
- B: (-2, -2)
- C: (-2, -5)
- D: (-7, -5)
For polygon A'B'C'D':
- A': (-1, 4)
- B': (-2, 2)
- C': (-5, 2)
- D': (-5, 7)
### Analyzing the points:
1. **A to A'**:
- A: (-4, -1) → A': (-1, 4)
- The x-coordinate changed from -4 to -1 (+3), and the y-coordinate changed from -1 to 4 (+5).
2. **B to B'**:
- B: (-2, -2) → B': (-2, 2)
- The x-coordinate remains the same, but the y-coordinate changed from -2 to 2 (+4).
3. **C to C'**:
- C: (-2, -5) → C': (-5, 2)
- The x-coordinate changed from -2 to -5 (-3), and the y-coordinate changed from -5 to 2 (+7).
4. **D to D'**:
- D: (-7, -5) → D': (-5, 7)
- The x-coordinate changed from -7 to -5 (+2), and the y-coordinate changed from -5 to 7 (+12).
### Looking for patterns:
- The changes in the coordinates suggest a combination of translation and possibly rotation, primarily because the coordinates of A and D change significantly.
### Rotation:
To check if it could be a 90° rotation, let's apply a 90° counterclockwise rotation to the original coordinates.
The rule for a 90° counterclockwise rotation is:
- (x, y) → (-y, x).
Let's rotate point A (-4, -1):
- A' = (1, -4) -- which does not match.
Continuing this for others doesn't give matching after rotation.
### Reflection:
If we reflect across the y-axis:
- (x, y) → (-x, y)
Rotating and reflecting didn't match up either as seen from analyses.
### Conclusion:
In context to made observations, the coordinates show more sign of translation rather than a clear reflection or rotation, so the transformation appears to be a **horizontal translation** (as others would not fit).
Therefore, the correct match of transformation for ABCD to A'B'C'D' is the **Horizontal translation.**