Question

What is the scale factor of the dilation?

Answer 1

The rule for dilation (scale factor k) about the origin is given by:
(x,y)->(kx,ky)

The scale factor k can be obtained from any one of the ratios:

`scale\, factor\, =\, k\, = (OD')/(OD)=(OE')/(OE)=(OF')/(OF)=(OG')/(OG)=(1)/(2)`

Answer 2

The scale factor of the dilation is
`(1)/(2)`.

Explanation:

From the given figure it is clear that the vertices of figure DEFG are D(4,8), E(8,8), F(8,6), G(4,6).

The vertices of image D'E'F'G' are D'(2,4), E'(4,4), F'(4,3), G'(2,3).

From the figure it is clear that DF=4 units and D'F'=2 units.

The scale factor is proportion of corresponding sides of image and preimage.

k=(D'F')/(DF)

Substitute DF=4 units and D'F'=2 units.

k=(2)/(4)

k =
`(1)/(2)`

Therefore the scale factor of the dilation is
`(1)/(2)`.