Question

For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____. -5 5 0.5 2

Answer 1

So the answer is 0.5

Explanation:

We'll assume the dilation was done at the origin point, so it was done evenly.

Since the k point went from (10,0) to (5,0), we know it was reduced... so the scale factor has to be below 1. A scale factor means the size wasn't changed and a dilation/scale factor larger than 1 means it was enlarged.

So, we take the new X-value (5) and divide it by the original X-value (10).

Scale factor = 5/10 = 1/2... so 0.5

Answer 2

The scale factor of the following dilation is, 0.5

Explanation:

The rule of dilation with scale factor k is given by:

`(x, y) \rightarrow (kx, ky)`

As per the statement:

Given the following dilation:

(10, 0) → (5, 0) .....[1]

We have to find the scale factor.

Using the above rule we have;

`(10, 0) \rightarrow (10k, 0k)`

Now compare this with equation [1] we have;

(10k, 0) = (5, 0)

⇒10k = 5

After solving we get;

`k = (1)/(2)=0.5`

Therefore, the scale factor of the following dilation is, 0.5