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Stretch With Invariant x Axis

When a figure is stretched, it is enlarged or reduced in on direction only – often the x or y direction. Stretches are defined in terms of a stretch factor and an invariant line.

In the diagram above, triangle ABC is stretched to form the triangle A'B'C'. The invariant line is shown with arrows. Every point on the line is unmoved.

If the invariant line is the x – axis the stretch is especially interesting and useful. A stretch of factor k with invariant line the x – axis is sent to the point (x,ky). The diagrams below indicate stretches in the y – direction (with invariant line the x – axis) with scale factors 2 and ½ respectively.