Detailed definition
Understanding Stretch
A stretch changes a figure more in one direction than in another. In coordinate work this often means scaling x-values or y-values differently, so the image looks pulled wider, taller, or more generally distorted along one direction.
Stretch is not a rigid motion because lengths and most angles do not stay the same. In many cases it is not even a similarity transformation, because different directions scale by different amounts.
This page keeps the original and stretched images together so you can study what remains aligned and what changes shape under nonuniform scaling.
Key facts
Important ideas to remember
- A stretch changes one direction more than another.
- A one-way stretch has an invariant direction or line that acts as the reference for the change.
- Parallel relationships often survive a stretch, but lengths and angle measures generally do not.
- Under coordinate stretching, circles can become ellipses and squares can become rectangles or other distorted images.
Where it is used
Where stretch shows up
- Use stretch when studying graph transformations that change one axis more than the other.
- Use it in modelling and design contexts where a shape is elongated horizontally or vertically.
- Use it to compare rigid and non-rigid transformations on the same coordinate plane.
Common mistakes
What to watch out for
- Do not call a stretch a dilation if the figure is not being scaled uniformly in all directions.
- Do not expect angle measures to stay fixed after a general stretch.
- Do not ignore which axis or direction is being stretched, because that decides the resulting shape.