Enlargements and stretches

Definition of Enlargements: An enlargement is a transformation that alters the size of a shape. The shape’s original structure and the relative proportions of its parts remain the same while the size changes.
Centre of Enlargement: The point from which the enlargement is performed is known as the centre of enlargement. If the scale factor is positive, then the image will be on the same side of the centre; if it is negative, the image will be on the opposite side.
Scale Factor: The amount by which the shape is enlarged or shrunk is determined by the scale factor. A scale factor of two, for example, doubles the size of the shape, whereas a scale factor of 0.5 halves it. A scale factor of -1 creates an image of the shape that is the same size but oriented in the opposite direction.
Enlargement Properties: After an enlargement, angles remain the same, and lengths are multiplied by the scale factor. The area is multiplied by the square of the scale factor, and the volume is multiplied by the cube of the scale factor.
Definition of Stretches: A stretch is a transformation that alters the shape of an object by stretching it in one direction typically along either the x-axis or y-axis.
Features of Stretches: When a shape is stretched, the lengths in one direction are altered, whereas the lengths in the perpendicular direction remain the same. This means that the shape’s overall structure transforms in a way that a simple enlargement might not capture.
Stretches and Coordinates: A stretch has a greater effect on the coordinates of the points in the shape than an enlargement. For example, a stretch in the x-direction by a scale factor of 2 would double all the x-coordinates of the atoms in the shape.
Invariant Line: In a stretch, the line in the direction perpendicular to the stretching direction is invariant, which means that all points that lie on that line will remain static.
Stretches and Scale Factors: While the length along the stretch direction will be multiplied by the scale factor, lengths perpendicular to that direction remain unchanged. For instance, if a rectangle is stretched in the horizontal direction by a scale factor of 2, its width will be doubled, but its height will stay the same.
Practice Problems: To gain a solid grasp of enlargements and stretches, it is recommended to work through a wide range of practice problems consisting of various scale factors and centre points. Remember to check solutions carefully to understand the principles behind every step and ensure accuracy.