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This is a tricky one.
I know an easy, but complicated way to do this.
Wanna try it?
ok lets see if i can follow that way
Never mind. I have a waaayyyyy easier way. But before I show you it, I need to explain how it works: Let's start off with this figure here: https://www.desmos.com/calculator/lttgxf6exs
Oops sorry wrong link
There's your figure.
Now, let's take the point (4,-3)
And expand it outwards along a line, like this: https://www.desmos.com/calculator/kvjqstpl7y If the take the distance between the point and the origin (0,0) like this: |dw:1447452783330:dw|
Are you following?
i cant read the drawing
It says if the distance between the point and the origin is n, then the translated points distance from the origin will be 4 * n
(if we are using a scale factor of 4)
ok i got that
To find n we need x and y.
what is x and y
So, if we let theta be the scale factor. The translated point will be: \[((x \times \theta),(y \times \theta)\]
So, for a scale factor of 4, we can find each translated vertex with (x*4),(y*4)
im confused where do you get x and y
x and y are what you use to get coordinates...
ok but what are referring to as x and y
Ok. Let me help you visualize. Instead of theta, let's use s to represent the scale factor.
https://www.desmos.com/calculator/vjvbnc5dnv The green points represent the preimage. The blue points represent the dilated image. S represents the scale factor. When we change s, we change the dilation. Play around with it a bit until you understand.
So it's just each coordinate times s. Take (4,-3) Translated, it will be (4*s,-3*s)
oh ok that made me understand better
if s is 4, then (4,-3) will become (16,-12)
Get it now?
Dismiss always helps me visualize these types of problems.
yeah let me try to get the rest
So, all you have to do is set the scale factor to 4 and get the coordinates using my handy function.
so the rest would be D (-4,16) A(-12,4) and C(8,12)
are those my answers ?
check with desmos: https://www.desmos.com/calculator/vjvbnc5dnv
s is set to 4
ok so the dilation image has the coodinates we just found
and those are our answers?