The formula to calculate the new coordinates after dilation is:
\[ (x', y') = (k \times x, k \times y) \]
Where:
A dilation rule in mathematics refers to a transformation that alters the size of a figure without changing its shape. It involves expanding or shrinking the figure from a fixed point, known as the center of dilation. The degree of dilation is determined by a scale factor. If the scale factor is greater than 1, the figure enlarges; if it’s between 0 and 1, the figure reduces in size. The distances between points in the figure are proportionally increased or decreased according to the scale factor.
Let's consider an example:
Using the formula to calculate the new coordinates after dilation:
\[ (x', y') = (2 \times 3, 2 \times 4) = (6, 8) \]
This demonstrates that with an original point at (3, 4) and a scale factor of 2, the new coordinates after dilation would be (6, 8).
