What is the image of a shape after enlargement by a scale factor of 0.5?

The image of a shape after enlargement by a scale factor of 0.5 is a smaller, similar shape.

When you enlarge a shape by a scale factor of 0.5, each side of the shape becomes half as long as it was originally. This means that the new shape will be similar to the original shape, maintaining the same proportions and angles, but it will be smaller. For example, if you start with a square that has sides of 4 cm, after enlargement by a scale factor of 0.5, each side will be 2 cm.

In mathematical terms, a scale factor of 0.5 means that every dimension of the original shape is multiplied by 0.5. This affects not only the lengths of the sides but also the area of the shape. The area of the new shape will be one-quarter of the original area because area scales with the square of the scale factor (0.5^2 = 0.25). So, if the original shape had an area of 16 cm², the new shape will have an area of 4 cm².

It's important to note that while the size of the shape changes, the angles within the shape do not. This is why the new shape is described as "similar" to the original shape. Similar shapes have the same angles and proportional side lengths, even though their sizes are different. This concept is crucial in many areas of geometry and helps in understanding how shapes can be transformed while preserving their fundamental properties.