Question

Point R (8, -3) is rotated 180 degrees and then dilated by a scale factor of 2. What is the new coordinate for R''?

Options:
Option 1: (-16, 6)
Option 2: (-8, 3)
Option 3: (16, -6)
Option 4: (8, -3)

Answer 1

The new coordinates of point R after a 180-degree rotation and dilation by a scale factor of 2 are (-16, 6). This is achieved by first changing the sign of the original coordinates and then doubling the resultant coordinates, leading to Option 1 being the correct answer.

Step-by-step explanation:

The student's question involves finding the new coordinates of a point after a 180-degree rotation followed by dilation with a scale factor of 2. Initially, we have point R with coordinates (8, -3). After a 180-degree rotation about the origin, the new coordinates R' become (-8, 3). This rotation changes the sign of both x and y coordinates because it essentially reflects the point across both axes.

To find the final coordinates R'', we then apply dilation with a scale factor of 2 to R'. Dilation involves multiplying each coordinate by the scale factor. Therefore, we multiply both coordinates of R' by 2, resulting in the new coordinates being (-16, 6), which is Option 1. This represents the final position of point R after the sequence of transformations.