Question

Need help with dilation!
http://prntscr.com/d88k8q

Answer 1

@zepdrix

Answer 2

@triciaal

Answer 3

@sshayer

Answer 4

one approach

basically each length will change by the dilation factor.
the center is (-8, 2) mark this spot. find the length of each point from the center multiply by the factor and that will be the new length

Answer 5

Okay thanks Triciaal! :)

Answer 6

I'll show you my result when I'm done, to make sure it's correct

Answer 7

Disclaimer: I am not the best geometry person ---one approach

Answer 8

Hey, how do you ask questions?
Really need help with a question!

Answer 9

So you said I have to multiply the length by the factor correct?
And how would I find the points for the dilation?

Answer 10

@triciaal

Answer 11

@poto
@triciaal gave you the geometric approach, i.e. working on the diagram.
Please post what you get.

If you wish, you could also calculate the results of the dilation (as a check) using the following procedure, which may seem complicated at the beginning, but very easy once you've seen the example.
When dilation is about the origin O, with a scale factor k, then the dilation is, as you probably already know:
\(D_k: (x,y)\rightarrow (kx,ky)\)
If the dilation is about the centre of dilation located at C(a,b), then we need to do three steps:
1. translate the coordinate origin O to the centre of dilation C, call the new origin O'.
2. dilate, using the D operator as above
3. move the translated origin O' back to O.

Recall that the translation operator, T, is given by:
\(T_{a,b}: (x,y)\rightarrow (x+a,y+b)\)

Then steps 1 to 3 above would read:
\(D_{k,a,b}: (x,y)\rightarrow T_{a,b}\circ D_{k} \circ T_{-a,-b}\)
where (a,b) is the centre of dilation, and k the scale factor
and note that composite transformation occur from right to left.

If we combine all the steps, we end up with a single transformation:
\(D_{k,a,b}: (x,y)\rightarrow (k(x-a)+a,~k(x-b)+b) \) which is relatively simple.
Example for the top vertex A(2,12)=A(x,y) and centre of dilation (a,b)=(-8,2), scale factor k=1/5 :
Then
\(A'(\frac{1}{5}(2-(-8))+(-8), \frac{1}{5}(12-2)+2)=(10/5-8,10/5+2)=(-6,4)\)
I'll leave it to you to finish off the other three points, by the geometric method or the transformation method.

Answer 12

Alright! Thanks Mathmate! :)

Answer 13

You're welcome! :)

Answer 14

Thank you @mathmate also another reminder how much I have forgotten
@Poto there is the shorter approach

Answer 15

@triciaal
The geometric approach is much easier to work on, and much more visual and hence helps understanding of the concept.
Please don't discount its value! The transformation approach was just another way to serve as a check.