To enlarge a shape by a scale factor of $2$, you need to double the distance from each point on the shape to the chosen center of enlargement.

When you enlarge a shape by a scale factor of $2$, each point on the shape is moved to a position that is twice as far from the center of enlargement. This center can be located inside, outside, or on the shape itself. For instance, consider a triangle where you select one of its vertices as the center of enlargement. You would measure the distance from this vertex to the other vertices, and then double these distances to determine the new positions of the vertices.

To perform this enlargement accurately, you can utilize a ruler and a compass. First, draw a line from the center of enlargement to each vertex of the shape. Measure the distance from the center to each vertex. Then, mark a point on this line that is $2$ times the measured distance from the center. The new points you create will represent the vertices of the enlarged shape. Connect these new vertices to form the enlarged shape, which will be similar to the original but twice as large in every dimension.

As an example, if you have a square with a side length of $3 \, \text{cm}$ and you enlarge it by a scale factor of $2$, the new square will have a side length of $6 \, \text{cm}$. Consequently, each point on the original square will be twice as far from the center of enlargement, resulting in an enlarged square that has an area four times greater than that of the original. This method is applicable to any shape, ensuring that the enlarged shape retains the same proportions as the original.