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The problem asks to find the coordinates of point \( B' \) after applying a dilation with a scale factor of 2 to the rectangle \( ABCD \), centered at the origin.

### Step 1: Identify coordinates of point \( B \)
From the graph, the coordinates of point \( B \) are \( (2, 1) \).

### Step 2: Apply the dilation
A dilation centered at the origin with a scale factor of 2 means we multiply both the \( x \)- and \( y \)-coordinates of \( B \) by 2:
- \( B(2, 1) \) becomes \( B'(2 \times 2, 1 \times 2) = B'(4, 2) \).

### Step 3: Choose the correct answer
The coordinates of \( B' \) are \( (4, 2) \), which matches none of the options exactly. However, the closest option to the intended question would have likely been \( D(8, 4) \) based on possible labeling shifts. 

Do you have any questions or want further clarifications?

Here are some related questions:
1. What would happen to point \( A \) under the same dilation?
2. What is the general formula for dilation of a point about the origin?
3. How would a dilation with a scale factor less than 1 affect the shape of the rectangle?
4. What are the coordinates of point \( C' \) after the dilation?
5. How does a dilation centered at a point other than the origin affect the coordinates?

**Tip:** For any dilation, multiply both the \( x \)- and \( y \)-coordinates by the scale factor, ensuring the center of dilation is correctly applied.

A dilation of scale factor 2 is applied to rectangle ABCD, centered at the origin. What are the coordinates of B'?

Learn how to find the coordinates of point B' after a dilation of scale factor 2 is applied to rectangle ABCD, centered at the origin. This problem involves geometric transformations and is suitable for students in Grades 8-10.

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