The Dilation of a Point Calculator is a computational tool designed to determine the new coordinates of a point after undergoing dilation. Dilation involves scaling an object up or down with respect to a fixed point known as the center of dilation. The calculator uses the following formula to perform the dilation:
New_x = Center_x + (Point_x - Center_x) * Scale_factor New_y = Center_y + (Point_y - Center_y) * Scale_factor
Where:
Center_xandCenter_yare the x and y coordinates of the center of dilation, respectively.Point_xandPoint_yare the x and y coordinates of the point to be dilated, respectively.Scale_factoris the scale factor of the dilation. If the scale factor is greater than 1, the point will dilate away from the center; if it’s between 0 and 1, the point will dilate towards the center.
Table of General Terms
| Term | Definition |
|---|---|
| Dilation | The process of resizing an object while maintaining its shape. |
| Scale Factor | A ratio that describes how much larger or smaller the dilation will be. |
| Center of Dilation | The fixed point around which dilation occurs. |
| Coordinates | Pairs of numbers that represent the location of a point in a coordinate plane. |
Example of Dilation of a Point Calculator
Let’s consider an example to understand how the Dilation of a Point Calculator works:
Suppose we have a point with coordinates (3, 5) and we want to dilate it with a scale factor of 2 around the center (0, 0). Using the formula mentioned above, we can calculate the new coordinates as follows:
New_x = 0 + (3 - 0) * 2 = 6 New_y = 0 + (5 - 0) * 2 = 10
So, after dilation, the new coordinates of the point will be (6, 10).
Most Common FAQs
Dilation in geometry refers to the transformation of an object by enlarging or reducing its size while maintaining its shape.
Dilation can be calculated using the Dilation of a Point Calculator, which utilizes the coordinates of the center of dilation, the point to be dilated, and the scale factor.
The scale factor determines the ratio of the size of the image to the size of the original object. It determines whether the dilation will result in enlargement or reduction of the object