In a dilation of triangle ABC with a scale factor of 2 and center at C, the sides of the image triangle A'B'C' are twice as long as the corresponding sides of ABC. The concept of parallelism is maintained, ensuring that each side of ABC has a parallel counterpart in A'B'C' after the dilation.
In a dilation of triangle ABC with a scale factor of 2 and center of dilation at point C, the key principles involve the proportional expansion of each side by a factor of 2.
This means that the corresponding sides of the image triangle A'B'C' are twice as long as those of the original ABC. The center of dilation, point C, serves as the anchor for this transformation.
Importantly, dilations preserve parallelism, maintaining the concept that sides of the image triangle parallel to the sides of the original triangle share the same slope.
Each side of triangle ABC has a corresponding side in image triangle A'B'C' that is parallel to it, forming three pairs of parallel sides. This geometric transformation underscores the proportional scaling and preservation of parallel relationships in dilations.
complete question should be:
Explain the key principles and outcomes of a dilation applied to triangle ABC with a scale factor of 2, where point C is the center of dilation. Discuss how the concept of parallelism is maintained in the sides of the image triangle A'B'C' relative to the original triangle ABC in this dilation.