A dilation is a transformation that changes the size of a figure but not its shape. It's like using a magnifying glass to enlarge or shrink an image. The center of dilation is a fixed point, and the scale factor determines how much the figure is enlarged or shrunk....
Types of Dilations
Dilations can be:
- Enlargement: If the scale factor is greater than 1, the figure is enlarged.
- Reduction: If the scale factor is between 0 and 1, the figure is shrunk.
Understanding Coordinate Transformations
When a figure is dilated, the coordinates of each point are multiplied by the scale factor. This means that the distance from the center of dilation to each point is multiplied by the scale factor.
Applying the Dilation to Find D'
In the given problem, ABCD is dilated by a factor of 2. This means that each coordinate of point D will be multiplied by 2 to find the corresponding coordinate of D'.
Finding the Coordinates of D'
Let's assume the coordinates of point D are (x, y). After dilation by a factor of 2, the coordinates of D' would be (2x, 2y).
Example
For example, if the coordinates of D are (3, 4), the coordinates of D' would be (6, 8). This is because each coordinate is multiplied by 2.
Visual Representation
Here's a visual representation of the dilation:
5 4 3 B 2 1 C -8 -7 -6 -5 -4 -3-2-10 1 2 3 4 5 6 7 8 9 10 11 3PA -2 7 T D D' = ([?], [ ]) Enter
Conclusion
Understanding dilations and how to apply them to coordinate transformations is essential in geometry. By multiplying each coordinate by the scale factor, we can find the new coordinates of a point after dilation. In this case, if ABCD is dilated by a factor of 2, the coordinates of D' would be (2x, 2y), where (x, y) are the coordinates of D.