Question
what is (3,-5) after a translation of 5 units left and 3 units down followed by a reflection over the y-axis.
Answers
GPT-4o mini
To determine the final position of the point \((3, -5)\) after the described transformations, we can follow the steps one by one.
1. **Translation of 5 units left and 3 units down:**
- Translating left means we subtract from the x-coordinate.
- Translating down means we subtract from the y-coordinate.
Starting with the point \((3, -5)\):
- \(x\) coordinate after moving left: \(3 - 5 = -2\)
- \(y\) coordinate after moving down: \(-5 - 3 = -8\)
So after the translation, the new point is \((-2, -8)\).
2. **Reflection over the y-axis:**
- Reflecting over the y-axis changes the sign of the x-coordinate.
For the point \((-2, -8)\):
- The reflection over the y-axis results in \((2, -8)\).
Thus, after performing the translation followed by the reflection, the final coordinates of the point are \((2, -8)\).
1. **Translation of 5 units left and 3 units down:**
- Translating left means we subtract from the x-coordinate.
- Translating down means we subtract from the y-coordinate.
Starting with the point \((3, -5)\):
- \(x\) coordinate after moving left: \(3 - 5 = -2\)
- \(y\) coordinate after moving down: \(-5 - 3 = -8\)
So after the translation, the new point is \((-2, -8)\).
2. **Reflection over the y-axis:**
- Reflecting over the y-axis changes the sign of the x-coordinate.
For the point \((-2, -8)\):
- The reflection over the y-axis results in \((2, -8)\).
Thus, after performing the translation followed by the reflection, the final coordinates of the point are \((2, -8)\).