Which of the following shows point D reflected across the y-axis and then translated by the rule (x - 1, y - 2)
To find the new coordinates of point D after it is reflected across the y-axis and then translated, you can follow these steps:
1. Start with the original coordinates of point D.
2. Reflect the coordinates across the y-axis by changing the sign of the x-value. For example, if the original coordinates of point D are (x, y), the reflected coordinates will be (-x, y).
3. Translate the reflected coordinates based on the given rule (x - 1, y - 2). To translate a point, you need to add or subtract the specified values from the x and y coordinates. For example, if the reflected coordinates are (-x, y), the translated coordinates will be (-x - 1, y - 2).
Now, let's apply these steps to the given options to find which one represents the final coordinates of point D.
Option A: (4, 3)
- Reflecting across the y-axis: (-4, 3)
- Translating by the rule (x - 1, y - 2): (-4 - 1, 3 - 2) = (-5, 1)
Option B: (-4, -1)
- Reflecting across the y-axis: (4, -1)
- Translating by the rule (x - 1, y - 2): (4 - 1, -1 - 2) = (3, -3)
Option C: (-5, -3)
- Reflecting across the y-axis: (5, -3)
- Translating by the rule (x - 1, y - 2): (5 - 1, -3 - 2) = (4, -5)
Option D: (5, 1)
- Reflecting across the y-axis: (-5, 1)
- Translating by the rule (x - 1, y - 2): (-5 - 1, 1 - 2) = (-6, -1)
Based on these calculations, the correct option is Option D which represents the final coordinates of point D after it is reflected across the y-axis and then translated by the rule (x - 1, y - 2).