Enlargements and Projections

Understanding Enlargements

Remember that an enlargement is a type of transformation in which the lengths of all sides of a shape are multiplied by the same scale factor.
Know that the scale factor is the ratio of the length of a side in the enlarged figure to the corresponding side’s length in the original figure.
Realise that a shape and its enlargement are similar—their angles are identical and their sides are proportional.

Understand that enlargements produce similar shapes with equal angles but lengths that are multiplied by a scale factor.
Note that if the scale factor is greater than 1, the shape is enlarged, and if the scale factor is less than 1 but greater than 0, the shape is reduced.
Grasp that whereas enlargements alter a shape’s size, they do not affect its orientation.
Keep in mind that the enlargement transformation is centred around a fixed point, and all the points on the shape move away from or towards this point in a straight line.

Be able to perform enlargements by multiplying the coordinates of each point by the scale factor for enlargements centred at the origin.
When the centre of enlargement is not at the origin, translate the shape so that the centre of enlargement is at the origin, perform the enlargement, and then translate back.
Practice visualising and drawing enlargements on a grid by using ray tracing—drawing straight lines from the centre of enlargement through each corner of the shape, then marking the new corners on these lines.

Apprehend that enlargements still apply in three-dimensional geometry, where all distances (including heights, depths and widths) are multiplied by the scale factor.
Understand that enlargements can also be applied in cylinder and cone coordinate systems, where the radial and angular coordinates are unchanged but the length is multiplied by the scale factor.

Recall that a projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the planes with parallel lines.
Recognize that projections can be visualised as the shadows or outlines created when light is shone onto an object.
Remember that whereas a projection may alter an object’s size and shape, parallel lines in the original figure remain parallel in the projection.
Understand the difference between orthogonal (or perpendicular) and oblique projections. In an orthogonal projection, the lines of projection are perpendicular to the projection plane, while in an oblique projection they are not.
Relate projections to real-world applications such as maps, computer graphics, and blueprints.