To perform each of the transformations on the point A (4,3), we can follow these steps:
1. Dilation by a factor of 3:
- Multiply both the x-coordinate and the y-coordinate of A by 3.
New coordinates: (4*3, 3*3) = (12, 9)
2. Translation 5 units to the right:
- Add 5 to the x-coordinate of A.
New coordinates: (12+5, 9) = (17, 9)
3. Reflection over the x-axis:
- Multiply the y-coordinate of A by -1.
New coordinates: (17, -9)
4. Reflection over the y-axis:
- Multiply the x-coordinate of A by -1.
New coordinates: (-17, -9)
5. Reflection over the line y=x:
- Swap the x-coordinate and the y-coordinate of A.
New coordinates: (-9, -17)
6. Translation 5 units to the left:
- Subtract 5 from the x-coordinate of A.
New coordinates: (-9-5, -17) = (-14, -17)
7. Dilation by a factor of 1/3:
- Multiply both the x-coordinate and the y-coordinate of A by 1/3.
New coordinates: (-14*(1/3), -17*(1/3)) = (-14/3, -17/3)
Rounding the coordinates to one decimal place: (-4.7, -5.7)
Therefore, the final transformed coordinates of point A are approximately (-4.7, -5.7).