Transformations, congruence, vectors and similarity Study Guide

Enlargement is a type of geometric transformation that changes the size of an object but not its shape. To fully describe an enlargement, two pieces of information are essential: the centre of enlargement and the scale factor.

The centre of enlargement is a fixed point from which all distances are measured. If the centre of enlargement is (x, y), then to enlarge a point (a, b) by a scale factor 'k', the new point (a', b') is found by the formula: (a', b') = (x + k(a - x), y + k(b - y)).

A scale factor describes how much the object will be enlarged or reduced. If the scale factor, 'k', is greater than 1, the object will get bigger. If 0 < k < 1, the object will get smaller (this is a reduction). If k is exactly 1, the object remains unchanged. If k is negative, the enlargement is inverted through the centre of enlargement. For example, a scale factor of -2 would enlarge the object by a factor of 2 and rotate it 180 degrees around the centre of enlargement.

When carrying out an enlargement, draw a line from the centre of enlargement through each vertex of the object. Measure the distance from the centre to each vertex. Multiply this distance by the scale factor to find the distance from the centre to the corresponding vertex of the image. The new vertices are plotted along the lines already drawn. Connecting these new vertices forms the enlarged or reduced image.

Enlargement is a type of transformation that changes the size of a shape but not its orientation or angles. It's like zooming in or out on an image. To perform an enlargement, you need two key pieces of information: a scale factor and a centre of enlargement. The scale factor tells you how much larger or smaller the new shape (the image) will be compared to the original shape (the object). If the scale factor is greater than 1, the shape gets larger. If the scale factor is between 0 and 1 (a fraction or decimal), the shape gets smaller. A negative scale factor means the shape is enlarged on the opposite side of the centre of enlargement and inverted. The centre of enlargement is a fixed point from which all points on the object are 'stretched' or 'shrunk' to create the image. To find the position of a point on the enlarged image, you draw a line from the centre of enlargement through each vertex of the object. Then, you measure the distance from the centre to the original vertex and multiply that distance by the scale factor to find the new position of the vertex along the line. Repeat this for all vertices, and then connect the new vertices to form the enlarged image.