https://file.aiquickdraw.com/mathbot/file/1726773417756h3prtjmj.jpg

The question in the image involves a dilation transformation applied to a figure \( JKLM \), where the figure is dilated by a scale factor of 2. We are tasked with finding the new coordinates of the transformed points \( J'K'L'M' \).

### Dilation Concept:
In a dilation, each point is moved farther from or closer to the origin by a certain scale factor. In this case, the scale factor is 2. The formula for dilation is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
where \( k \) is the scale factor (here \( k = 2 \)) and \( (x, y) \) are the original coordinates.

### Step-by-step calculation:

#### Original coordinates of \( J, K, L, M \):
From the graph:
- \( J(x_J, y_J) = (-1, -1) \)
- \( K(x_K, y_K) = (-3, -3) \)
- \( L(x_L, y_L) = (1, 1) \)
- \( M(x_M, y_M) = (2, 2) \)

#### Applying dilation by 2:
- \( J' = (2 \cdot (-1), 2 \cdot (-1)) = (-2, -2) \)
- \( K' = (2 \cdot (-3), 2 \cdot (-3)) = (-6, -6) \)
- \( L' = (2 \cdot 1, 2 \cdot 1) = (2, 2) \)
- \( M' = (2 \cdot 2, 2 \cdot 2) = (4, 4) \)

### New coordinates:
- \( J' = (-2, -2) \)
- \( K' = (-6, -6) \)
- \( L' = (2, 2) \)
- \( M' = (4, 4) \)

Now, let's match these results with the given answer choices:
- **Correct Answer**: \( J' (-2, -2), K' (-6, -6), L' (2, 2), M' (4, 4) \)

Would you like more details on dilation transformations, or have any other questions? Here are 5 related questions to explore further:

1. What happens when the dilation scale factor is less than 1?
2. How do dilations differ from translations and rotations?
3. Can dilations be applied to figures not centered at the origin?
4. How would the dilation change if the scale factor was negative?
5. How do dilations affect the area and perimeter of a shape?

**Tip**: When performing dilation, always multiply both the x and y coordinates of each point by the scale factor to find the transformed points.

Figure JKLM is dilated by a scale factor of 2. What are the new coordinates for J'K'L'M' after the transformation?

Explore how to apply dilation to figure JKLM with a scale factor of 2. Learn step-by-step how to calculate the new coordinates for J', K', L', and M' using the dilation formula (x', y') = (k * x, k * y). Suitable for students in Grades 7-10.

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