Question

What is the rule for the following dilation? A(-5.8) B(13.65, 12.8) C(-9, -13) D(0, 12) A'(-2.5, 4) B'(6.825, 6.4) C'(-4.5, -6.5) D'(0, 6) O Scale Factor: 1.5 O Scale Factor: 2 O Scale Factor: 5 O Scale Factor: 0.5

Answer 1

(D)Scale Factor: 0.5​

Step-by-step explanation:

The coordinates A,B, C and D are those of the pre-image while A',B',C' and D' are those of the image.

Using the coordinates of A and A'

Let the scale factor = k

On the x-axis:

`\begin{gathered} -5k=-2.5 \\ k=(-2.5)/(-5)=0.5 \end{gathered}`

Similarly, on the y-axis

`\begin{gathered} 8k=4 \\ k=(4)/(8) \\ k=0.5 \end{gathered}`

We conclude that the scale factor is 0.5