Question

In the diagram , ABCD is dilated about point E to form A'B'C'D'. What is the scale factor of the dilation ?

Answer 1

Consider the given figures ABCD and A'B'C'D'.

The side AB is 4 units, while side A'B' is 2 units, so the scale factor is given by,

`SF=\frac{A^(\prime)B^(\prime)}{AB^{}}=(2)/(4)=(1)/(2)`

Thus, the scale factor of the dilation is 1/2.

Note that the scale factor can be calculated by taking the ratio of any two corresponding sides i .e.

`SF=(A^(\prime)B^(\prime))/(AB)=(B^(\prime)C^(\prime))/(BC)=(C^(\prime)D^(\prime))/(CD)=(A^(\prime)D^(\prime))/(AD)`