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Mathematics 22 Online
Astrid1:

Can Ne1 explain if i got this right? And if i did... Can u explain how i figured it out?

Astrid1:

darkknight:

We need to see the question, all we see are your answers.

Astrid1:

There are questions there.....What is the center of the dilation? Explain how you know. And the second one was....Which triangle is the original and which triangle is the dilation? Explain how you know.

darkknight:

the center of dilation is where the shape is either expanded or shrunken, for example, if we had the shapes |dw:1605824553922:dw|

Astrid1:

yeah... A dilation changes the size and shape of the object

darkknight:

sorry my drawing skills aren't perfect, but in the case above, the red shape is a dilated figure of the black rectangle, so from the center of dilation is where the shape is dilated from, like the shape being dilated produces another shape that is either expanded, and shrunked from that point

Astrid1:

Thats okay... Yur very smart OwO

darkknight:

lol, so what did you say was the center of dilation?

Astrid1:

I said that the center of dilation was between D and E

darkknight:

hmm, why would you say that? just out of curiosity

Astrid1:

Becuase its where everything connects,,, Im kinda stupid ,,,,

darkknight:

No you are not stupid, but yes that is not the correct reasoning. So to find the point of dilation, do you remember the figure I drew for you before

Astrid1:

Yeah

darkknight:

Suppose we take another figure, but put the center of dilation at the red dot, (indicated in pic) |dw:1605825214585:dw| Is this correct in this case? i s the dilatd ed

darkknight:

my keyboard stop ped working hold on 1 min

Astrid1:

Okay

darkknight:

Okay, anyways look at that drawing above, if the red dot is the center of dilation for the black triangle, can the yellow triangle be produced?

Astrid1:

Errr.. Uhmmmm..... I dont know..... Hmmmmmmm Im gonna say.....No?

darkknight:

No it isn't, because from the center of dilation, the figure is expanded/shrunk from that ratio in all directions. For example, If we draw a square (black) with length 3, than we set the center of dilation to the middle(and dilate by 2), the dilated figure would look like this (red) |dw:1605825501458:dw| But if that same center of dilation were at a different point, the dilated figure would look like this |dw:1605825565118:dw|

darkknight:

So you are correct, the answer is no in this case for my question. Now back to your question, the center of dilation can't be between D and E, because if the figure were dilated from that point, we wouldn't get triangle ABL, so the center of dilation is actually at point A

darkknight:

@Astrid1

darkknight:

We have triangle AED and triangle ABL, so basically, these 2 triangles are just dilated from the point A, do you see why?

Astrid1:

Hmmmmm..... Yeah....

darkknight:

also, dilation means that a figure is either stretched or shrinked, so the second question is kinda weird, because technically both triangles could be the original and both could be dilations of the other. Like if ALB is the original then ADE is the dilation (a shrink) and if ADE is the original than ALB is the dilation (an expansion).

Astrid1:

OwO ur smartttt

darkknight:

alright, have a good day

Astrid1:

U too! :)

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