Geometry

Question Analysis

The main focus is to apply a dilation with a scale factor of 6, centered at the origin, to Point E, whose coordinates are , and find its new coordinates.

Key Concept Explanation

For a dilation centered at the origin, if a point  is dilated by a scale factor , the new coordinates  are calculated using the formula . When k>1, it results in an enlargement of the point.

Step - by - Step Solution

1. Given the coordinates of Point E as  and the scale factor .

2. Calculate the new  - coordinate:

Using the formula , substitute  and , we get

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