As you can see, the two shapes are similar in that their corresponding angles are all congruent, but they are different in that their corresponding sides are different lengths. The image gives us the center of dilation, but it does not give us the scale. To find the scale, we must look at two corresponding sides. In this example, we have a 6 as the original image and a 12 as the dilated image. Because our original image is smaller than the dilation, we know the scale factor will be greater than 1. (If we reversed the roles and our larger image was our original, our resulting image would be smaller, a reduction, and have a scale of less than 1.) To find our scale we can use the equation 6*X=12 and solve for X. This dilation must have a scale factor of 2. This means that the dilated image sides should all be twice the length of the original image. If we were looking for the center of dilation, we would need to know the scale. Since our scale is 2, that means that the distance from our center of dilation to our dilated image needs to be twice as far as the length from the center of dilation to our original image.
I think typing out the rules for dilation helped me to understand them a little better, maybe reading them will have the same affect for you! If not, there is an awesome video that takes dilation and explains it in its simplest form and why we need to understand it here.
Ok, I seriously laughed out loud at your decision between if pupil dilation or math dilations are worse. I think it's math.. but that's just me, haha. Anyways this is still a math concept that challenges me and even more so when I have to read how to do it. I am very much someone that has to see it or do it, otherwise I don't understand. But however, you gave a great explanation as to how to find the dilation or reduction of an image.
ReplyDeleteYour part on how a dilated image should be twice the length of the original image actually helped me understand the concept a little bit more than I did before reading this. Sometimes it helps to learn from someone in the same place as you, you get a different side of it, not so much someone that has mastered the concept already.
VIDEOS like the one you posted are always very helpful and needed for someone like me too. Great job!
Hey Allison!
ReplyDeleteIt sounds funny but it's actually helpful that you made any kind of connection between something you know (getting your eyes dialated) and then dialation in terms of math. It's obvously not the exact same thing, but i think that even having that base for what the concept is probably helped you! As long as you have something to compare it to, like having side A on both shapes, once you figure out the relationship between those two, apply that to all sides to get te results of the full dialation!