## anonymous one year ago In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Where is point A' and D' located at??

1. anonymous

this is the graph

2. e.mccormick

When you dialate with a factor of 2, do you know what you do to the points?

3. anonymous

no i dont understand at all. its my first day veiwing geometry

4. e.mccormick

Well, dialate can sort of be explained as scaling. If I scale a drawing it means to change the size. That help?

5. anonymous

yea but what do i do with the points, do i divide or anything is there an equation??

6. e.mccormick

Well, the factor is what the change in size is. You do not devide by it when going from the original to the changed one.

7. e.mccormick

|dw:1435471251448:dw| If a is a 1 by 1 box and b is a 4 by 4 box, then a is dialated to b by multiplying all points by 4. However, if I wanted to dialate from b to a I would multiply all points by \(\tfrac{1}{4}\).

8. anonymous

so in this problem would I multiply all the points by 1/2??

9. e.mccormick

No. They gave you a factor of 2. So it needs to double in size.

10. anonymous

so i multiply the points. so the word dilate could also mean to get bigger in size??

11. e.mccormick

Yes, you multiply. Dialate means scale or change in size. If you scale by \(\tfrac{1}{4}\) then it would get smaller. So it can be bigger or smaller. It just depends on if the factor is greater than one or between 0 and 1.

12. anonymous

OMG THANKS SO MUCH! i got it righ!

13. anonymous

right*

14. e.mccormick

Some examples here too: http://regentsprep.org/regents/math/geometry/GT3/indexGT3.htm But yah, once you get the idea that the dialation fact is the key for how much bigger or smaller it is, then it begins to make sense. Oh, and you can end up with fractions that make it bigger, like \(\tfrac{3}{2}\). It is more than 1 since it is 3 halfs, so it would still make it bigger.

15. e.mccormick

So, what points did you get for A' and D' in (x,y) form?

16. anonymous

i got -2,-2 and 4,-2

17. e.mccormick

Yep. So you understand it just fine as far as I can see. =)

18. anonymous

thanks so much!

19. e.mccormick