Answer:
The pre image is a factor 2 bigger, and there fore it's endpoints a' and b' must also be a factor 2 further away from the center 2,0.
Step-by-step explanation:
This is a long explanation. I did my best to guide you through all the steps needed to answer the question, because it almost instantly happens in my mind. Writing down these "reasoning steps", hopefully can give you some insight in understanding what I am asking myself to finally solve the problem. I hope it helps you, and that you can learn from it.
The pre image is the original image, which is NOT visible. Because original image is not visible, that makes it a little tricky, because you have to "imagine" an image that is not there...
Please understand what is described:
The original was dilated at a scale factor of 1/2 from center 2,0 and <em>that result</em> is now visible as An, which has endpoints located at a and b.
So, the big "problem" is to understand what effect the dialated scale factor of 1/2 has, when it was applied to the ORIGINAL.
You ask yourself, was the original bigger or was the original smaller? If you CONCLUDE that the scaling factor 1/2 must <em>result</em> in a SMALLER image, then the original, then you can finally conclude that the original image must have been bigger to make that happen.
Ok, so the pre image was bigger...
How much bigger was the pre image, <em>when you know a dialation scale factor of 1/2 was used to form the endpoints a and b...</em>
Well, now you ask yourself, by what amount do you need to multiply the scale factor 1/2 to get to 2/2 (which is 1 by the way). You do this, because you want to know how big the original must have been, and the original can be "reconstructed" by "reversing" the dialation the other way around. In other words <em>by what amount do you need to multiply the scale factor 1/2 to get to 2/2</em>.
Since 2 * 1/2 = 1, then the original image can be formed from the given image by applying a dialation factor of 2.
So now we know that the original must have been BIGGER by a factor 2.
Finally, do not forget to mention that ORRIGINAL endpoints, a' and b', MUST also be a factor 2 further away from the center 2,0.
So now you have your answer. I hope it helps.
