Question

Quadrilateral rust has a vertex at r (1, 5). what are the coordinates of r' after the translation (x, y) → (x + 1, y – 1), followed by a dilation by a scale factor of 2, centered at the origin?

a. (4, 4)
b. (2, 8)
c. (3, 9)
d. (4, 8)

Answer 1

To find the coordinates of r' after the translation and dilation, follow the steps mentioned.Option D is the correct answer.

Step-by-step explanation:

To find the coordinates of r' after the translation and dilation, we can follow these steps:

1. Apply the translation (x, y) → (x + 1, y – 1) to the vertex r(1, 5) to get the new coordinates r'(2, 4).
2. Next, apply the dilation by a scale factor of 2 centered at the origin to r'.
3. Multiply the x-coordinate and y-coordinate of r' by 2 to get the final coordinates of r' after dilation, which are (4, 8).

To determine the coordinates of r' following the translation and dilation operations, a systematic approach is applied. Firstly, the translation (x, y) → (x + 1, y – 1) is employed on the vertex r(1, 5), resulting in the updated coordinates r'(2, 4). Subsequently, a dilation with a scale factor of 2, centered at the origin, is implemented on r'.

By multiplying both the x-coordinate and y-coordinate of r' by 2, the final coordinates of r' post-dilation are derived as (4, 8). These sequential transformations provide a comprehensive understanding of the geometric changes undergone by the point r during the translation and dilation processes.