Geometry

Question Analysis

This question focuses on finding the coordinates of a point  after dilation. The key is to use the formula for dilation with a given center of dilation  and scale factor .

Key Concept Explanation

The formula for dilation of a point  with center of dilation  and scale factor  is . This formula accounts for the change in position based on the distance from the center of dilation and the scale factor.

Step - by - Step Solution

1. Identify the values: Here, , , , , and .

2. Calculate the  - coordinate of :

Use the formula .

Substitute the values: .

First, calculate inside the parentheses: .

Then, .

Finally,

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