Geometry

Question Analysis

This question focuses on dilation. The main task is to determine the scale factor of the dilation centered at the origin by comparing the coordinates of the original points (A, B, C) and their dilated counterparts (A', B', C').

 

Key Concept Explanation

For dilation centered at the origin, if a point  is dilated to , the scale factor  is calculated as  (when  and ).

 

Step - by - Step Solution

1. Using point A and A':

Given  and .

Using the  - coordinates: .

Using the  - coordinates: .

2. Using point B and B':

Given