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 3, centered at the origin?

a. (6, 12)
b. (4, 14)
c. (6, 4)
d. (3, 12)

Answer 1

The coordinates of r' after the translation and dilation are (6, 12). Option A is the correct answer.The coordinates of r' after translation and dilation are (6, 12), as confirmed by option a.

Step-by-step explanation:

To find the coordinates of r' after the translation and dilation, we need to apply the translation and dilation operations to the vertex r(1, 5).

Translation: (x, y) → (x + 1, y – 1)

1. Translate the x-coordinate by adding 1: 1 + 1 = 2
2. Translate the y-coordinate by subtracting 1: 5 - 1 = 4

The new coordinates after translation are r'(2, 4).

Dilation: Scale factor of 3, centered at the origin

1. Multiply the x-coordinate by the scale factor: 2 * 3 = 6
2. Multiply the y-coordinate by the scale factor: 4 * 3 = 12

The final coordinates after dilation are r'(6, 12).

Therefore, the coordinates of r' after the translation and dilation are (6, 12), option a.

The transformation of the vertex r(1, 5) involves both translation and dilation. By applying the translation (x, y) → (x + 1, y – 1), the coordinates are shifted to r'(2, 4). Subsequently, the dilation with a scale factor of 3, centered at the origin, modifies the coordinates to r'(6, 12). This process ensures accurate positioning after the specified transformations, and the resulting coordinates are consistent with option a.