https://file.aiquickdraw.com/mathbot/file/1726761707383o68jr20a.jpg

The image shows a triangle \( \triangle MLK \) with points \( M \), \( L \), and \( K \) located at coordinates approximately:

- \( M(-3, 1) \)
- \( L(2, 1) \)
- \( K(1, -2) \)

The task is to dilate this figure by a factor of 4 centered at the origin.

### To perform a dilation:
Given that the dilation is centered at the origin with a scale factor of 4, the coordinates of each point will be multiplied by 4. The new coordinates for each point after dilation are calculated as follows:

1. **Point M**: 
   \[
   (-3, 1) \rightarrow (-3 \times 4, 1 \times 4) = (-12, 4)
   \]
   
2. **Point L**: 
   \[
   (2, 1) \rightarrow (2 \times 4, 1 \times 4) = (8, 4)
   \]

3. **Point K**: 
   \[
   (1, -2) \rightarrow (1 \times 4, -2 \times 4) = (4, -8)
   \]

### The new triangle \( \triangle M'L'K' \) has vertices:
- \( M'(-12, 4) \)
- \( L'(8, 4) \)
- \( K'(4, -8) \)

To complete the transformation, you can plot these new points on the graph.

Would you like further assistance or clarification on any step? Here are a few additional related questions to explore:

1. How would the triangle change if the dilation factor were negative?
2. What is the effect of dilating the triangle around a different center, say \( (2, 2) \)?
3. How does the area of the triangle change after dilation by a factor of 4?
4. Can you calculate the distances between the original and dilated points?
5. What would the result be if the dilation factor were \( \frac{1}{2} \)?

**Tip**: When dilating figures on a coordinate plane, always multiply both the x and y coordinates by the scale factor!

The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image.

Learn how to dilate a triangle with vertices M(-3,1), L(2,1), and K(1,-2) by a factor of 4 centered at the origin. This geometry problem explains the dilation process step-by-step, covering key concepts in coordinate geometry and dilation transformations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation