Final answer:
The question involves enlarging a point using a scale factor of -2 and a given center of enlargement. The process includes finding the difference between the original point and the center, multiplying by the scale factor, and adding back to the center to find the new coordinates. The calculation must be applied to each given option to determine the correct enlarged point.
Step-by-step explanation:
To enlarge a point by a scale factor with respect to a center of enlargement, we must follow specific mathematical steps to find the new coordinates. The scale factor of -2 means that the image will be twice as far from the center of enlargement as the original point but in the opposite direction.
Let's take point a) (2, -5) as an example. To enlarge this point using (6,5) as the center of enlargement with a scale factor of -2, calculate the difference between the point's coordinates and the center's coordinates:
- Δx = 2 - 6 = -4
- Δy = -5 - 5 = -10
Then multiply these differences by the scale factor of -2:
- Δx' = -2 * -4 = 8
- Δy' = -2 * -10 = 20
Add these new differences to the center of enlargement (6,5) to find the new coordinates of the enlarged point:
- X' = 6 + 8 = 14
- Y' = 5 + 20 = 25
The new enlarged point coordinates are (14, 25), which is not one of the options provided. This process must be done for each point to determine which one is correct. The calculation should be repeated for the rest of the points, and the correct option should match the resulting coordinates.