1)To find a Scale factor of Dilation, about the origin
We have
Pre-mage Image
(x, y) k(x,y)
For example
Pre-image Image
(2,4) 2(2,4) = (4,8)
2)When it's not about the origin then we have to count from the Projection Point
Having said this, ex
Which is not a step
a)
We can divide the x value of the image over the pre-image, not the way around.
In the example, I've given if we divide the pre-image over the image value we would have found a scale factor of 1/2. In the example, The scale factor was the inverse: 2
Answer:
r = 
Step-by-step explanation:
So we need to complete the square for both parts of the equation
First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6
So first we can complete the square for x² + 2x
To do so we need to use
to figure out the number we need to add to both sides
In this case our b is 2, so substituting this in we get 
Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1
Now we can follow the same steps to complete the square for y² + 4y
Here our b is 4, so substituting this in we get 
Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4
Now condensing everything we have (x + 1)² + (y + 2)² = 11
The formula for a circle is (x - h)² + (y - k)² = r²
In our equation we have r² = 11
To find the radius we need to take the square root of both sides
to get r = 
All of the answer choices that you are given are incorrect. I have calculated it in all different ways and get the same thing and it is none of those. The correct answer would be -75 though.
I think A since working backwards and looking for a pattern wouldn't help, maybe C but im not sure