How do you enlarge a shape by a scale factor of 2?

To enlarge a shape by a scale factor of 2, double the distance from each point to the centre.

When you enlarge a shape by a scale factor of 2, you are essentially making every point on the shape twice as far from a chosen centre of enlargement. This centre can be a point inside, outside, or on the shape itself. For example, if you have a triangle and you choose one of its vertices as the centre of enlargement, you will measure the distance from this vertex to each of the other vertices and then double these distances to find the new positions of the vertices.

To do this accurately, you can use a ruler and a compass. First, draw a line from the centre of enlargement to each vertex of the shape. Measure the distance from the centre to each vertex, then mark a point on the line that is twice this distance from the centre. These new points will be the vertices of the enlarged shape. Connect these new vertices to form the enlarged shape, which will be similar to the original shape but twice as large in every dimension.

For example, if you have a square with a side length of 3 cm and you enlarge it by a scale factor of 2, the new square will have a side length of 6 cm. Each point on the original square will be twice as far from the centre of enlargement, resulting in a square that is four times the area of the original. This method works for any shape, ensuring that the enlarged shape maintains the same proportions as the original.