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Dilation Rule Calculator

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Dilation Rule Calculator

Enter any 2 values to calculate the required value

Enter any two values (original coordinates, scale factor, or new coordinates) to determine the missing value using the dilation formula.

The Dilation Rule Calculator assists in calculating the transformation of a point under dilation. Dilation in geometry involves resizing a figure proportionally about a center point, determined by the scale factor (k).

This tool is particularly useful for scaling geometric shapes, analyzing transformations, and solving mathematical problems related to coordinate geometry.

Formula

The dilation formulas are as follows:

  1. New x-coordinate (x’): x=kxx’ = k \cdot x
  2. New y-coordinate (y’): y=kyy’ = k \cdot y
  3. Scale Factor (k): k=xx or k=yyk = \frac{x’}{x} \text{ or } k = \frac{y’}{y}
  4. Original Coordinates: x=xk,  y=ykx = \frac{x’}{k}, \; y = \frac{y’}{k}

Solved Examples

Example 1: Calculate New Coordinates
Original coordinates: x=5,y=6x =
Scale factor: k

Step Value Explanation
Formula (x’): x=kxx’ = k \c Scale x-coordinate
Calculation: x=25=10x’ = 2 \cdot New x-coordinate = 10
Formula (y’): y=kyy’ = k \ Scale y-coordinate
Calculation: y=26=12y’ = 2 \cdot New y-coordinate = 12

Example 2: Calculate Scale Factor
Original coordinates: x=8,y=10x = 8, y
New coordinates: x=16,y=20x’ = 16, 

Step Value Explanation
Formula (k): k=xxk = \frac{x Calculate scale factor from x
Calculation: k=168=2k = \frac{16 Scale factor = 2

Applications

  • Geometry: Resizing figures or analyzing geometric transformations.
  • Graphics and Design: Proportionally scaling objects in digital tools.
  • Mathematics: Solving problems related to similar figures and transformations.

FAQs

What is a scale factor in dilation?
The scale factor (k) determines how much a figure is enlarged or reduced. Values greater than 1 enlarge, while values less than 1 reduce.

What happens if the scale factor is negative?
A negative scale factor reflects the figure across the center of dilation.

Can this calculator handle real-world measurements?
Yes, the formulas are versatile and can handle any units, as long as they remain consistent throughout.

Simplify geometric transformations with the Dilation Rule Calculator. Calculate new coordinates, scale factor, or original points effortlessly.

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