What is the length of segment A'E'? So as I was mentioning while I read it, they didn't actually draw this one out. So we are told that pentagon A'B'C'D'E' is the image, and they don't, they haven't drawn that here, is the image of pentagon ABCDE under a dilation withĪ scale factor of 5/2. So once again you see our scale factor being 1/3. Here between A' and E', our change in y is negative one, which is 1/3 of negative three, and our change in x is one, which is 1/3 of three. Three right over here, and our change in x is So if you looked at the distance between point A and point E, our change in y is negative You didn't have a vertical or a horizontal line? Well one way to think about it is, the changes in y and the changes in x would scale accordingly. That was pretty straightforward because we had a very clear, you could just see theĭistance between A and B. So our scale factor right over here is 1/3. Over here is equal to two, and so you can see we went from having a length of six to a length of two, so you would have to multiply by 1/3. Now what about the corresponding side from A' to B'? Well this length right So this length right over here is equal to six. Well this is one, two, three, four, five, six. What is our distance? Our change in y is our distance because we don't have a change in x. What is our change in y? Our change in, or even When you do a dilation, the distance between corresponding points will change according to the scale factor. Out the scale factor you just have to realize The center of the dilation, but in order to figure What is the scale factor of the dilation? So they don't even tell us Is 4, times 3 is 12.- We are told that pentagon A'B'C'D'E', which is in red right over here, is the image of pentagon ABCDE under a dilation. 6 plus 2 is 8, times 3 isĢ4, divided by 2 is 12. The areas of the small and the large rectangle. Like this that is exactly halfway in between Something like that, and you're multiplying That looks something like- let me do this in orange. Take the average of the two base lengths andĪnother interesting way to think about it. Let's just add up the two base lengths, multiply that times the The bases times the height and then take the average. Ways to think about it- 6 plus 2 over 2, and Then all of that over 2, which is the same Think of it as this is the same thing as 6 plus 2. The height, and then you could take the average of them. So when you think aboutĪn area of a trapezoid, you look at the two bases, the It's going to be 6 times 3 plusĢ times 3, all of that over 2. Halfway between the areas of the smaller rectangleĪnd the larger rectangle. Sense that the area of the trapezoid, thisĮntire area right over here, should really just And it gets half theĭifference between the smaller and the larger on The smaller rectangle and the larger one on Of the area, half of the difference between Yellow, the smaller rectangle, it reclaims half The trapezoid, you see that if we start with the Halfway in between, because when you look at theĪrea difference between the two rectangles- and let Now, it looks like theĪrea of the trapezoid should be in between The area of a rectangle that has a width of 2Īnd a height of 3. We went with 2 times 3? Well, now we'd be finding Now, the trapezoid isĬlearly less than that, but let's just go with So it would give us thisĮntire area right over there. The area of a figure that looked like- let me do We multiply 6 times 3? Well, that would be the Multiplied this long base 6 times the height 3? So what do we get if Is, given the dimensions that they've given us, what And so this, byĭefinition, is a trapezoid. Where two of the sides are parallel to each other.
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