Question

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

Answer 1

Answer:

The scale factor is $\frac{1}{2}$.

Step-by-step 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

$k=\frac{5}{10}$

$k=\frac{1}{2}$

Therefore the scale factor is $\frac{1}{2}$.

Answer 2

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