To calculate the scale factor of a dilation, divide the coordinates of the new image (after dilation) by the coordinates of the original image. This ratio represents the scale factor.
The Scale Factor Dilation Calculator calculates the scale factor in dilations, commonly used in geometry to resize shapes while preserving their proportions. This process involves enlarging or shrinking an object from a central point, called the center of dilation.
To know the scale factor is essential for accurately transforming figures on a coordinate plane, allowing precise calculations for similar shapes in math and practical applications.
Formula:
| Variable | Description |
|---|---|
| Original coordinates | |
| Dilated coordinates | |
| Scale factor of dilation |
Solved Calculations
Example 1:
| Step | Calculation |
|---|---|
| Original Coordinates (X1, Y1) | (2, 3) |
| Dilated Coordinates (X2, Y2) | (6, 9) |
| Scale Factor Calculation | |
| Result | Scale factor is 3 |
Answer: The scale factor of dilation is 3.
Example 2:
| Step | Calculation |
|---|---|
| Original Coordinates (X1, Y1) | (4, 5) |
| Dilated Coordinates (X2, Y2) | (8, 10) |
| Scale Factor Calculation | |
| Result | Scale factor is 2 |
Answer: The scale factor of dilation is 2.
What is Scale Factor Dilation Calculator?
The Scale Factor Dilation Calculator is a specialized tool. It is used for calculating the dilated size of a shape based on a given scale factor. In geometry, dilation involves resizing a figure from a specific center point without altering its shape.
This calculator enables users to determine how much larger or smaller a shape becomes after applying the dilation scale factor, a valuable calculation in fields like geometry and design.
For input, specify the original coordinates or dimensions of the figure and the desired scale factor. For instance, when dilating a triangle by a factor of 2, each side doubles, maintaining proportionality. This tool streamlines the scaling process by providing accurate results for a variety of shapes and transformations.
Final Words:
Finally, the Scale Factor Dilation Calculator simplifies complex geometric transformations, making it a practical resource for students and professionals exploring dilations and similar figures.
