The problem asks for the image of point $B(2, 3)$ after a dilation of scale factor 3, centered at the origin.

Explanation:

To find the new coordinates of a point after a dilation:

1. Multiply the $x$- and $y$-coordinates of the point by the scale factor.
2. The formula is: $(x', y') = (k \cdot x, k \cdot y)$ where $k$ is the scale factor, and $(x, y)$ are the original coordinates.

Solution:

• The original coordinates of $B$ are $(2, 3)$.
• The scale factor is $3$.
• Using the formula: $(x', y') = (3 \cdot 2, 3 \cdot 3) = (6, 9)$

Thus, the image of point $B$ after the dilation is $\mathbf{(6, 9)}$.

The correct answer is: D. (6, 9)

Let me know if you want further clarification or a detailed explanation of the dilation concept.

Here are 5 related questions to expand your understanding:

1. What are the new coordinates of $A(1, 1)$ after the same dilation?
2. How would the dilation change if the center was not at the origin?
3. Can you determine the coordinates of $C(4, 1)$ after the same dilation?
4. How does a scale factor of less than 1 (e.g., $\frac{1}{2}$) affect the coordinates?
5. What would happen if the scale factor were negative (e.g., $-3$)?

Tip:

Always remember that a dilation centered at the origin preserves the proportional relationship between all points but scales them by the given factor.