Question

Determine the coordinates of the image of D(4, −3) after (x, y) → (x + 3, y) (-3, 7) (7, 3) (-7, -3) (3, -7) (3, 7) (7, -3) (-7, 3)

Answer 1

The image of point D(4, -3) after the given transformations is (3, -7).

Step-by-step explanation:

To determine the coordinates of the image of point D(4, -3) after the given transformations, we need to apply each transformation one by one.

1. Transformation (x, y) -> (x + 3, y): (4+3, -3) = (7, -3)
2. Transformation (-3, 7): Reflects the point across the y-axis to (-7, -3)
3. Transformation (7, 3): Reflects the point across the x-axis to (-7, 3)
4. Transformation (-7, -3): Reflects the point across the y-axis to (7, -3)
5. Transformation (3, -7): Reflects the point across the line y = x to (-7, 7)
6. Transformation (3, 7): Translates the point 3 units to the right to (10, 7)
7. Transformation (7, -3): Reflects the point across the line y = x to (-3, 7)
8. Transformation (-7, 3): Reflects the point across the line y = x to (3, -7)

Therefore, after applying all the transformations, the coordinates of the image of point D(4, -3) are (3, -7).