Question

For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.

Answer 1

scale factor is equal to 1/2, since the point went from 10 to 5

Answer 2

The scale factor is
`(1)/(2)`.

Explanation:

The dilation of a point about the origin with scale factor k is defined as

`P(x,y)\rightarrow P'(kx,ky)` ..... (1)

It means the scale factor is calculated as

`k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}`

The given dilation is defined as

`(10,0)\rightarrow (5,0)` ..... (2)

From (1) and (2) we get,

x coordinate of image = 5

x coordinate of preimage = 10

`k=(5)/(10)`

`k=(1)/(2)`

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