Geometry

Question Analysis

This question focuses on applying the concept of dilation with a negative scale factor. The key is to use the formula for dilation centered at the origin to find the new coordinates of the point.

Key Concept Explanation

Dilation centered at the origin multiplies the coordinates of a point  by the scale factor . When  is negative,  in addition to changing the size of the figure, it also reflects the figure across the origin. The formula for dilation centered at the origin is .

Step - by - Step Solution

1. Given the point  and scale factor .

2. Use the dilation formula .

For the  - coordinate of : Multiply the  - coordinate of  by . So,