https://file.aiquickdraw.com/mathbot/file/1729201028604do9zwa5u.jpg

The problem asks to **dilate** the point \( L(-1, -4) \) by a scale factor of 0.5, about the point \( (-1, -4) \). Let's break it down:

### Step 1: Understand the problem
- **Dilation**: This is a transformation that resizes the points. In this case, the scale factor is 0.5, which means the new point will be half the distance from the center of dilation.
- **Center of dilation**: The dilation happens about the point \( (-1, -4) \), which is the same as the original point \( L \).
  
### Step 2: Apply dilation
Since the point of dilation \( (-1, -4) \) is the same as the point \( L \), any dilation will leave the point unchanged. This is because there's no distance to resize when the point coincides with the center of dilation.

Thus, the dilated point \( L' \) will remain at the same coordinates:
\[
L'(-1, -4)
\]

### Answer: The correct location for \( L' \) is \( (-1, -4) \).

Would you like more details on dilation or transformations? Here are some related questions you might explore:

1. What happens to points when dilating by a scale factor greater than 1?
2. How do you find the image of a point after dilation with a different center?
3. Can dilation result in points being moved farther away? How?
4. What is the general formula for dilating points in a plane?
5. How does dilation affect shapes such as triangles or circles?

Tip: When the point of dilation is the same as the point being dilated, the point remains unchanged no matter the scale factor!

Dilate the point L(-1, -4) by a scale factor of 0.5, about the point (-1, -4). Where is L' located?

Learn how to dilate point L(-1, -4) by a scale factor of 0.5 around the center (-1, -4). Understand how the dilation transformation works when the point and the center coincide.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation