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The problem asks for the coordinates of \( B' \) after a dilation of triangle \( ABC \) with a scale factor of 3. The original coordinates of \( B \) are \( B(3, -2) \).

A dilation with a scale factor \( k \) multiplies both the \( x \)- and \( y \)-coordinates of a point by \( k \). Therefore, for point \( B(3, -2) \) with a scale factor of 3, the coordinates of \( B' \) will be:

\[
B'(x', y') = (3 \times 3, 3 \times -2) = (9, -6)
\]

Thus, the coordinates of \( B' \) are \( (9, -6) \).

The correct answer is \( (9, -6) \), which matches the third option.

Would you like further details on dilation or any other part of this concept?

Here are five questions that extend this concept:
1. What are the coordinates of \( A' \) after a dilation with the same scale factor?
2. How would the coordinates of \( C' \) change with a scale factor of 2 instead of 3?
3. What happens to the shape and size of a triangle after a dilation?
4. How would you reverse a dilation? What is the scale factor needed for that?
5. What is the effect of a negative scale factor on dilation?

**Tip**: To perform dilations, always multiply both coordinates of a point by the scale factor.

Triangle ABC has coordinates A(2,2), B(3,-2) and C(4,-3). What are the coordinates of B' after a dilation with a scale factor of 3?

Solve a geometry problem involving the dilation of triangle ABC with a scale factor of 3. Learn how to calculate the new coordinates of B' using the dilation formula, and explore how dilations affect geometric shapes. Suitable for students in Grades 8-10.

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