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What are the coordinates of *L* if it is dilated with a scale factor of 3 about the origin?

The point \( L \) in the graph appears to have coordinates \( (5, 2) \).

To find the coordinates of point \( L \) after it is dilated with a scale factor of 3 about the origin, we apply the following rule for dilation:

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

where \( (x, y) \) are the original coordinates, \( k \) is the scale factor, and \( (x', y') \) are the new coordinates after dilation.

Given:
- Original coordinates \( (x, y) = (5, 2) \)
- Scale factor \( k = 3 \)

The new coordinates after dilation are:

\[
(x', y') = (3 \cdot 5, 3 \cdot 2) = (15, 6)
\]

So, the coordinates of point \( L \) after dilation are \( (15, 6) \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What happens to the distance between the origin and a point after dilation?
2. How would the coordinates change if the scale factor was negative?
3. What is the effect of dilation on the shape of a polygon?
4. How do you dilate a point if the center of dilation is not the origin?
5. What is the relationship between the scale factor and the area of a shape after dilation?

**Tip:** When dilating a point, the origin remains fixed, and all other points move along the line that connects them to the origin, with their distances from the origin multiplied by the scale factor.

Learn how to find the coordinates of a point after dilation with a scale factor of 3 about the origin. This problem covers the concept of dilation in geometry, with a step-by-step solution using the dilation formula. Suitable for students in Grades 7-9.

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