Cotangent

Enlargement, sometimes called scaling or dilation, is a kind of transformation that changes the size of an object. The image created is similar to the object.

length of side in image = length of side in object x scale factor

Despite the name enlargement, it includes making objects smaller because the shape can be bigger or smaller according to the scale factor, k.

distance from centre of enlargement to point on image = distance from centre of enlargement to point on object x scale factor

With a negative scale factor the number part of it tells us if the shape is to be made bigger or smaller, while the negative sign tells us that the image and object are on opposite sides of the centre of enlargement.

Find the scale factor:

We know that k<1, because the image is smaller than the object.

Perform a dilation centered at (0,0), where k=3/2

Solution:

A(2,8) A'(3,12) B(10,4) B'(15,6) C(6,2) C'(9,3) Graphycally: