To apply the dilation rule, multiply the coordinates of the original point by the scale factor to get the new coordinates.
The Dilation Rule Calculator simplifies calculating the transformed coordinates of a shape or point after applying a dilation. This process scales a figure either up or down relative to a fixed point (the center of dilation), maintaining its proportionality.
Vastly used in geometry, algebra, and graphing, this calculator is helpful for analyzing transformations with specific scale factors, including fractions and whole numbers. It supports applications in academics and design, ensuring precise results for scaling figures, triangles, or points.
Formula
(x′, y′) = (k ∗ x, k ∗ y)
| Variable | Description |
|---|---|
| (x′, y′) | Transformed coordinates after dilation |
| k | Scale factor |
| (x, y) | Original coordinates of the point or shape |
Solved Calculations
Example 1:
| Input | Value |
|---|---|
| Original Point (x, y) | (4, 6) |
| Scale Factor (k) | 2 |
| Formula Used | (x′, y′) = (2 ∗ 4, 2 ∗ 6) |
| Transformed Point (x′, y′) | (8, 12) |
Example 2:
| Input | Value |
|---|---|
| Original Point (x, y) | (-3, 5) |
| Scale Factor (k) | 0.5 |
| Formula Used | (x′, y′) = (0.5 ∗ -3, 0.5 ∗ 5) |
| Transformed Point (x′, y′) | (-1.5, 2.5) |
What is the Dilation Rule Calculator?
The Dilation Rule Calculator is a helpful tool. It is used for applying geometric dilations by calculating the transformation of points, shapes, or graphs using a given scale factor.
This calculator is widely used in geometry and algebra to find new coordinates or dimensions of figures after dilation, either enlarging or reducing them proportionally.
It can solve queries like how to calculate dilation factor, what is the rule for this dilation, or how to dilate a triangle by 3/2. It supports various input formats, such as fractions, decimals, or whole numbers, and accounts for different centers of dilation, whether at the origin or elsewhere. This tool also provides results for more advanced calculations, like the dilation of functions and graphs.
Additionally, it simplifies complex concepts, such as finding the scale factor of dilation or transforming coordinates according to the dilation formula. Whether you’re working with points, triangles, or custom shapes, this tool ensures accurate and quick results for all dilation-related tasks.
Final Words:
Ultimately, the Dilation Rule Calculator is an essential resource for mastering geometric transformations. It simplifies complex operations, making it ideal for students, educators, and professionals alike.
