Math Problem Statement

The figure below is dilated by a factor of 5/4 centered at the origin. Plot the resulting image.

Solution

It looks like you are working on a problem involving dilations on the coordinate plane. The image shows a figure that is to be dilated by a factor of 54\frac{5}{4}, centered at the origin.

To plot the resulting image of the dilation:

  1. Each point of the original figure will be multiplied by 54\frac{5}{4} to find its new position.
  2. For example, if a point (x,y)(x, y) is on the original figure, the new coordinates will be (54x,54y)\left( \frac{5}{4}x, \frac{5}{4}y \right).

If you need help with specific points or have any further questions about the process, feel free to ask! Would you like more details on how to apply the dilation step by step?

Here are some related questions:

  1. What does it mean to apply a dilation to a figure on the coordinate plane?
  2. How can you determine the coordinates of a point after dilation?
  3. What is the difference between enlargement and reduction when performing a dilation?
  4. How do you find the center of dilation in a geometric transformation?
  5. What are the effects of a dilation factor greater than 1 versus less than 1?

Tip: Double-check your calculations after dilating the points to ensure the figure maintains its proportionality and shape!

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Math Problem Analysis

Mathematical Concepts

Dilations
Coordinate Plane
Scaling

Formulas

Dilation formula: (x', y') = (k * x, k * y), where k is the dilation factor

Theorems

Properties of dilations
Dilation centered at the origin

Suitable Grade Level

Grades 7-9