Question
A coordinate plane's x-axis ranges from negative 12 to 1 and its y-axis ranges from negative 6 to 7, both by 1-unit increments. 6 points are marked and plotted forming 2 triangles, 1 solid and 1 dotted.
What kind of translation has been made to triangle ABC ?
What kind of translation has been made to triangle ABC ?
Answers
GPT-4o mini
To determine what kind of translation has been made to triangle ABC, we need to know the original coordinates of triangle ABC and the coordinates of the translated triangle. A translation can be characterized by the movement of points in a specific direction.
A translation involves shifting all points in the triangle by the same horizontal and vertical distance. Here are the steps to analyze it:
1. **Identify Original Coordinates**: Obtain the original coordinates of triangle ABC. This is crucial to establish where it started.
2. **Identify Translated Coordinates**: Obtain the coordinates of the translated triangle. This is usually marked with different points (e.g., triangle XYZ).
3. **Calculate the Differences**: To find the translation vector, subtract the corresponding coordinates of the original triangle from the coordinates of the translated triangle. The translation vector can be represented as \( (a, b) \) where:
- \( a = x_{new} - x_{old} \)
- \( b = y_{new} - y_{old} \)
4. **Interpret the Vector**: The values of \( a \) and \( b \) will tell you how far and in what direction the triangle was moved.
- If \( a \) is positive, the triangle moved right; if negative, it moved left.
- If \( b \) is positive, the triangle moved up; if negative, it moved down.
5. **Resulting Translation**: Write down the translation as "triangle ABC was translated by (a, b)."
Without specific coordinates, it is not possible to determine the exact translation. However, if you have those coordinates, you can follow the steps above to find the translation type. If you provide the coordinates, I can assist you with the specific translation.
A translation involves shifting all points in the triangle by the same horizontal and vertical distance. Here are the steps to analyze it:
1. **Identify Original Coordinates**: Obtain the original coordinates of triangle ABC. This is crucial to establish where it started.
2. **Identify Translated Coordinates**: Obtain the coordinates of the translated triangle. This is usually marked with different points (e.g., triangle XYZ).
3. **Calculate the Differences**: To find the translation vector, subtract the corresponding coordinates of the original triangle from the coordinates of the translated triangle. The translation vector can be represented as \( (a, b) \) where:
- \( a = x_{new} - x_{old} \)
- \( b = y_{new} - y_{old} \)
4. **Interpret the Vector**: The values of \( a \) and \( b \) will tell you how far and in what direction the triangle was moved.
- If \( a \) is positive, the triangle moved right; if negative, it moved left.
- If \( b \) is positive, the triangle moved up; if negative, it moved down.
5. **Resulting Translation**: Write down the translation as "triangle ABC was translated by (a, b)."
Without specific coordinates, it is not possible to determine the exact translation. However, if you have those coordinates, you can follow the steps above to find the translation type. If you provide the coordinates, I can assist you with the specific translation.