Question

Given a dilation with the origin O (0, 0), by observation determine the scale factor "K."

Answer 1

Answer:

The correct option is 1. The scale factor is 1/2.

Step-by-step explanation:

The given rule of dilation is

$D_{o,K}:(6,12)\rightarrow (3,6)$

Where, o is origin or center of dilation and K is scale factor.

If a figure is dilation by scale factor K and center of dilation at origin, then

$P(x,y)\rightarrow P'(kx,ky)$

It means

$\text{Scale Factor}=\frac{\text{x-coordinate of image}}{\text{x-coordinate of preimage}}$

$K=\frac{3}{6}$

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

The scale factor is 1/2. Therefore the correct option is 1.

Answer 2

When the dilation is about the origin, the scale factor multiplies every coordinate. That is (considering the x-coordinate) ...
  6·k = 3
  k = 3/6 = 1/2

The appropriate choice is
  1. 1/2