A dilation of point \( R(-4, -2) \) with a scale factor of \( \frac{5}{2} \) involves multiplying both coordinates of the point by the scale factor. The formula for dilation is:

\[
R'(x', y') = \left( k \cdot x, k \cdot y \right)
\]

where \( k \) is the scale factor, and \( (x, y) \) is the original point. In this case, the scale factor \( k = \frac{5}{2} \), and the original coordinates are \( (-4, -2) \).

Now, let's calculate the new coordinates:

\[
x' = \frac{5}{2} \times (-4) = \frac{-20}{2} = -10
\]
\[
y' = \frac{5}{2} \times (-2) = \frac{-10}{2} = -5
\]

Thus, the new point \( R' \) after the dilation is \( (-10, -5) \).

Would you like more details or have any questions? Here are some related questions to think about:

1. What is the general formula for dilation in geometry?
2. How does a dilation with a scale factor greater than 1 affect a figure?
3. How would a dilation with a scale factor less than 1 change the coordinates?
4. What happens if the scale factor is negative in a dilation?
5. Can you apply dilation to figures other than points?

**Tip**: Dilation preserves the shape of a figure but changes its size based on the scale factor.

Discover how to dilate point R(-4, -2) with a scale factor of 5/2 using the dilation formula. This geometry problem illustrates key concepts in transformations and changes in size while preserving shape. Suitable for Grades 8-10 students learning about dilation and geometric transformations.

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