stuck-help
  • stuck-help
The endpoints of line AB are A(9,4) and B(5,-4). The endpoints of the image after a dilation are A(6,3) and B(3,-3). Find the scale factor and explain each of your steps
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
malcolmmcswain
  • malcolmmcswain
Ok, let's graph this, and see if it can help you visualize it.
malcolmmcswain
  • malcolmmcswain
The points are plotted here: https://www.desmos.com/calculator/mclsqhwnkc
malcolmmcswain
  • malcolmmcswain
What do you notice?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

stuck-help
  • stuck-help
the first one is longer than the dialation one
malcolmmcswain
  • malcolmmcswain
Well, yeah. The red points are the endpoints of the translated segment.
malcolmmcswain
  • malcolmmcswain
I mean, how do you think we could find the scale of dilation?
stuck-help
  • stuck-help
yes i got that
malcolmmcswain
  • malcolmmcswain
The scale of dilation is, for example, take: (x*3,y*3) The dilation is a scale of 3 (x*?,y*?) How do you think we can find the scale of dilation for this problem?
stuck-help
  • stuck-help
i dont know how to find the scale factor but i know it is less than 1
malcolmmcswain
  • malcolmmcswain
You're already on the right track.
malcolmmcswain
  • malcolmmcswain
I'm going to edit the coordinates on desmos a bit to help you visualize it.
stuck-help
  • stuck-help
ok
malcolmmcswain
  • malcolmmcswain
Ok, look on desmos
stuck-help
  • stuck-help
this is what i got graphing the coordinates
malcolmmcswain
  • malcolmmcswain
Look at the bottom
malcolmmcswain
  • malcolmmcswain
There are little sliders
malcolmmcswain
  • malcolmmcswain
Where it says n1 = 1 and n2 =1
malcolmmcswain
  • malcolmmcswain
If you play around with those, you can see the dilations visually.
malcolmmcswain
  • malcolmmcswain
Try and find A(6,3) and B(3,-3)
stuck-help
  • stuck-help
im confused what are we looking at
malcolmmcswain
  • malcolmmcswain
Do you see the little sliders that say n1 = 1 and n2 =1
malcolmmcswain
  • malcolmmcswain
On desmos
malcolmmcswain
  • malcolmmcswain
https://www.desmos.com/calculator/mclsqhwnkc
stuck-help
  • stuck-help
no
malcolmmcswain
  • malcolmmcswain
See it in the lower left corner?
malcolmmcswain
  • malcolmmcswain
I built a little dilation playground for you to help you understand :P if you play around with those sliders, you can see the dilations real time
stuck-help
  • stuck-help
i dont have those on my screen
malcolmmcswain
  • malcolmmcswain
Oh, sorry there's a new link: https://www.desmos.com/calculator/qjmzzqfz46
malcolmmcswain
  • malcolmmcswain
Try now.
malcolmmcswain
  • malcolmmcswain
Click and drag the sliders to see the dilations.
stuck-help
  • stuck-help
ok i got them now so what am i doing with them
malcolmmcswain
  • malcolmmcswain
If you move the sliders around, you can visualize the dilations.
malcolmmcswain
  • malcolmmcswain
So, using these points do you think we can create A(6,3) and B(3,-3)?
stuck-help
  • stuck-help
im getting the red coordinates not the green
stuck-help
  • stuck-help
wait nevermind
malcolmmcswain
  • malcolmmcswain
Look, you have to move the sliders:
stuck-help
  • stuck-help
i got that but this is very confusing i cant get the sliders to the right coordinates
malcolmmcswain
  • malcolmmcswain
That's right.
malcolmmcswain
  • malcolmmcswain
We can't
malcolmmcswain
  • malcolmmcswain
Why?
stuck-help
  • stuck-help
ok ?
malcolmmcswain
  • malcolmmcswain
(By the way, sorry I'm dragging this out. I just want you to understand this thoroughly.)
malcolmmcswain
  • malcolmmcswain
(and I also want it to be fun :P)
malcolmmcswain
  • malcolmmcswain
Anyway, clearly we can't just multiply x and y by certain numbers to dilate certain figures.
malcolmmcswain
  • malcolmmcswain
Here's why.
malcolmmcswain
  • malcolmmcswain
When you multiply x and y by different variables, you assume that (0,0) (the origin) is the center of dilation.
malcolmmcswain
  • malcolmmcswain
If you can't multiply these variables, though, the only answer is, the origin is not our center point for dilation...
malcolmmcswain
  • malcolmmcswain
Which means, to figure out our scale of dilation, we can't just find these numbers, we're going to have to use ratios.
stuck-help
  • stuck-help
that makes no sense and i have to write down all my steps to find my scale factor and i cant do that doing it this way
malcolmmcswain
  • malcolmmcswain
Don't worry, you'll be able to.
malcolmmcswain
  • malcolmmcswain
All we have to do is find the center of the dilation, then we can find the scale easily.
malcolmmcswain
  • malcolmmcswain
Let me show you.
malcolmmcswain
  • malcolmmcswain
I'm sorry if this is confusing you :(
stuck-help
  • stuck-help
i just have no idea and i have alot going on in my head so its hard to focus on this but i have to do it
malcolmmcswain
  • malcolmmcswain
I'm so sorry. Look here: https://www.desmos.com/calculator/lttgxf6exs This is how I found the center of dilation. I just drew lines that went from the first A to the second A, and from the first B to the second B, and where they intersect must be the center of dilation.
malcolmmcswain
  • malcolmmcswain
So, the center is (-3,0)
malcolmmcswain
  • malcolmmcswain
Now, to find the scale.
stuck-help
  • stuck-help
ok
malcolmmcswain
  • malcolmmcswain
I haven't done this in a while, but I think it's just the slopes of the line...
stuck-help
  • stuck-help
i dont understand why we need those lines what are they what do they do to find the scale factor
malcolmmcswain
  • malcolmmcswain
So, I think it's (A*1/3) and (B*-1/2)
malcolmmcswain
  • malcolmmcswain
Let's check.
stuck-help
  • stuck-help
but what are the steps to get to that
malcolmmcswain
  • malcolmmcswain
Ugh... I'm so sorry stuck... I'm kinda lost. I'm trying, but I haven't done problems like this in a while. :( I think I may need some help.
malcolmmcswain
  • malcolmmcswain
I'm doing something wrong here.
malcolmmcswain
  • malcolmmcswain
@lochana Can you help me with this question?
malcolmmcswain
  • malcolmmcswain
He seems knowledgable about dilations.
malcolmmcswain
  • malcolmmcswain
I'm better with the basic matrix transformations.
malcolmmcswain
  • malcolmmcswain
I guess we'll just have to wait for @lochana because I want to make sure I'm not giving out incorrect answers. I just need to make sure I'm not giving out false answers.
malcolmmcswain
  • malcolmmcswain
That is the last thing I would want @stuck-help :(
stuck-help
  • stuck-help
thats fine i think im going to take a break for a little bit
malcolmmcswain
  • malcolmmcswain
Ok... once again, sorry...
lochana
  • lochana
it is a strange one:)
malcolmmcswain
  • malcolmmcswain
I know, right?
malcolmmcswain
  • malcolmmcswain
I found the center of dilation, but wasn't sure what to do from there... :P
malcolmmcswain
  • malcolmmcswain
https://www.desmos.com/calculator/lttgxf6exs
lochana
  • lochana
I think you can tackle it only by considering length of each line
malcolmmcswain
  • malcolmmcswain
OH YEAH
malcolmmcswain
  • malcolmmcswain
WHY DIDNT I THINK OF THAT?!?
lochana
  • lochana
[\scale = \frac{length of AB after slcaled}{length of AB before scaled}\]
malcolmmcswain
  • malcolmmcswain
I was like taking the slopes of the lines and saying, ok so its 1/3 and -1/2 but you can just use pythagorean theorem to find the lengths of the lines and then divide.
lochana
  • lochana
\[scale = \frac{length of AB after slcaled}{length of AB before scaled}\]
lochana
  • lochana
yeah. you can do in that way too. but you have to be wet little bit:)
malcolmmcswain
  • malcolmmcswain
So, to find the lengths we can just use pythagorean theorem. \[AB = \sqrt{4^2+8^2}\] \[A'B' = \sqrt{3^2+6^2}\]
lochana
  • lochana
\[AB length(before) = \sqrt{45}\]\[AB length(after) = \sqrt{80}\]\[scale = \frac{\sqrt{80}}{\sqrt{45}} = \frac{4}{3}\]
lochana
  • lochana
exactly
malcolmmcswain
  • malcolmmcswain
Thank you so much for the clarification ^_^
malcolmmcswain
  • malcolmmcswain
I was struggling so much with this... :P
lochana
  • lochana
you are welcome:)
lochana
  • lochana
ah that's fine. it is a good thing:)
malcolmmcswain
  • malcolmmcswain
I was on the right track, but there was a much simpler route.
malcolmmcswain
  • malcolmmcswain
So, @stuck-help, there's your answer.
stuck-help
  • stuck-help
@malcolmmcswain |dw:1447444777875:dw| is this the start to it
malcolmmcswain
  • malcolmmcswain
That's right...
malcolmmcswain
  • malcolmmcswain
Finding the lengths.
stuck-help
  • stuck-help
ok so how did you get that
stuck-help
  • stuck-help
where did you get those numbers and why are we squaring
malcolmmcswain
  • malcolmmcswain
You know the pythagorean theorem right?
malcolmmcswain
  • malcolmmcswain
a^2+b^2=c^2
stuck-help
  • stuck-help
yes some what i do
stuck-help
  • stuck-help
|dw:1447445361887:dw| am i on the right track
malcolmmcswain
  • malcolmmcswain
Ok, we're using the pythagorean theorem to find the lengths here. Look: |dw:1447445266671:dw| To find the length of this segment, we have to first create a right triangle: |dw:1447445348550:dw| Then, we assume the segment is c, the hypoteneuse, and we can solve for c using the pythagorean theorem. |dw:1447445420882:dw| So, the length of this line is \[c=\sqrt{a^2+b^2}\]
malcolmmcswain
  • malcolmmcswain
Also, yes, you're on the right track.
stuck-help
  • stuck-help
ok so how does the pythagorean theorem play to this
stuck-help
  • stuck-help
and where do you get the 4 and 8 squared and 3 and 6 squared
malcolmmcswain
  • malcolmmcswain
https://learnzillion.com/lesson_plans/6406-find-the-length-of-a-line-segment-on-the-coordinate-plane-using-the-pythagorean-theorem
stuck-help
  • stuck-help
ok so do we do thins for both lines
stuck-help
  • stuck-help
ok so i got the 4 and 8 squared
stuck-help
  • stuck-help
@malcolmmcswain one thing has got me confused
stuck-help
  • stuck-help
1 Attachment
malcolmmcswain
  • malcolmmcswain
Ok, so that's just for finding the scale.
malcolmmcswain
  • malcolmmcswain
It's comparing them as a ratio to see how much we decreased.
stuck-help
  • stuck-help
ok but they are backwards do is it suppose to 3/4 of 4/3 because i thought it was less then one
malcolmmcswain
  • malcolmmcswain
Yeah, that's right. He made a mistake.
stuck-help
  • stuck-help
and how do you get 3 and 4 becasue im getting 6 and 8 so 3/4
malcolmmcswain
  • malcolmmcswain
6/8 simplifies to 3/4
stuck-help
  • stuck-help
oh ok not sure who i should metal here both of you were big help thank you so much
malcolmmcswain
  • malcolmmcswain
No problem. If anybody, medal lochana. I don't need a medal, and he really deserves it.
stuck-help
  • stuck-help
i would metal both becasue he helped you to the answer and me of course but you answered all my extra question thanks you both
malcolmmcswain
  • malcolmmcswain
Happy to help! ^-^

Looking for something else?

Not the answer you are looking for? Search for more explanations.