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

- stuck-help

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- malcolmmcswain

Ok, let's graph this, and see if it can help you visualize it.

- malcolmmcswain

The points are plotted here:
https://www.desmos.com/calculator/mclsqhwnkc

- malcolmmcswain

What do you notice?

Looking for something else?

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

## More answers

- stuck-help

the first one is longer than the dialation one

- malcolmmcswain

Well, yeah. The red points are the endpoints of the translated segment.

- malcolmmcswain

I mean, how do you think we could find the scale of dilation?

- stuck-help

yes i got that

- 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

i dont know how to find the scale factor but i know it is less than 1

- malcolmmcswain

You're already on the right track.

- malcolmmcswain

I'm going to edit the coordinates on desmos a bit to help you visualize it.

- stuck-help

ok

- malcolmmcswain

Ok, look on desmos

- stuck-help

this is what i got graphing the coordinates

##### 1 Attachment

- malcolmmcswain

Look at the bottom

- malcolmmcswain

There are little sliders

- malcolmmcswain

Where it says n1 = 1
and n2 =1

- malcolmmcswain

If you play around with those, you can see the dilations visually.

- malcolmmcswain

Try and find A(6,3) and B(3,-3)

- stuck-help

im confused what are we looking at

- malcolmmcswain

Do you see the little sliders that say n1 = 1 and n2 =1

- malcolmmcswain

On desmos

- malcolmmcswain

https://www.desmos.com/calculator/mclsqhwnkc

- stuck-help

no

- malcolmmcswain

See it in the lower left corner?

##### 1 Attachment

- 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

i dont have those on my screen

- malcolmmcswain

Oh, sorry there's a new link: https://www.desmos.com/calculator/qjmzzqfz46

- malcolmmcswain

Try now.

- malcolmmcswain

Click and drag the sliders to see the dilations.

- stuck-help

ok i got them now so what am i doing with them

- malcolmmcswain

If you move the sliders around, you can visualize the dilations.

- malcolmmcswain

So, using these points do you think we can create A(6,3) and B(3,-3)?

- stuck-help

im getting the red coordinates not the green

- stuck-help

wait nevermind

- malcolmmcswain

Look, you have to move the sliders:

##### 1 Attachment

- stuck-help

i got that but this is very confusing i cant get the sliders to the right coordinates

- malcolmmcswain

That's right.

- malcolmmcswain

We can't

- malcolmmcswain

Why?

- stuck-help

ok ?

- malcolmmcswain

(By the way, sorry I'm dragging this out. I just want you to understand this thoroughly.)

- malcolmmcswain

(and I also want it to be fun :P)

- malcolmmcswain

Anyway, clearly we can't just multiply x and y by certain numbers to dilate certain figures.

- malcolmmcswain

Here's why.

- malcolmmcswain

When you multiply x and y by different variables, you assume that (0,0) (the origin) is the center of dilation.

- malcolmmcswain

If you can't multiply these variables, though, the only answer is, the origin is not our center point for dilation...

- 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

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

Don't worry, you'll be able to.

- malcolmmcswain

All we have to do is find the center of the dilation, then we can find the scale easily.

- malcolmmcswain

Let me show you.

- malcolmmcswain

I'm sorry if this is confusing you :(

- 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

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

So, the center is (-3,0)

- malcolmmcswain

Now, to find the scale.

- stuck-help

ok

- malcolmmcswain

I haven't done this in a while, but I think it's just the slopes of the line...

- stuck-help

i dont understand why we need those lines what are they what do they do to find the scale factor

- malcolmmcswain

So, I think it's (A*1/3) and (B*-1/2)

- malcolmmcswain

Let's check.

- stuck-help

but what are the steps to get to that

- 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

I'm doing something wrong here.

- malcolmmcswain

@lochana Can you help me with this question?

- malcolmmcswain

He seems knowledgable about dilations.

- malcolmmcswain

I'm better with the basic matrix transformations.

- 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

That is the last thing I would want @stuck-help :(

- stuck-help

thats fine i think im going to take a break for a little bit

- malcolmmcswain

Ok... once again, sorry...

- lochana

it is a strange one:)

- malcolmmcswain

I know, right?

- malcolmmcswain

I found the center of dilation, but wasn't sure what to do from there... :P

- malcolmmcswain

https://www.desmos.com/calculator/lttgxf6exs

- lochana

I think you can tackle it only by considering length of each line

- malcolmmcswain

OH YEAH

- malcolmmcswain

WHY DIDNT I THINK OF THAT?!?

- lochana

[\scale = \frac{length of AB after slcaled}{length of AB before scaled}\]

- 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

\[scale = \frac{length of AB after slcaled}{length of AB before scaled}\]

- lochana

yeah. you can do in that way too. but you have to be wet little bit:)

- 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

\[AB length(before) = \sqrt{45}\]\[AB length(after) = \sqrt{80}\]\[scale = \frac{\sqrt{80}}{\sqrt{45}} = \frac{4}{3}\]

- lochana

exactly

- malcolmmcswain

Thank you so much for the clarification ^_^

- malcolmmcswain

I was struggling so much with this... :P

- lochana

you are welcome:)

- lochana

ah that's fine. it is a good thing:)

- malcolmmcswain

I was on the right track, but there was a much simpler route.

- malcolmmcswain

So, @stuck-help, there's your answer.

- stuck-help

@malcolmmcswain |dw:1447444777875:dw| is this the start to it

- malcolmmcswain

That's right...

- malcolmmcswain

Finding the lengths.

- stuck-help

ok so how did you get that

- stuck-help

where did you get those numbers and why are we squaring

- malcolmmcswain

You know the pythagorean theorem right?

- malcolmmcswain

a^2+b^2=c^2

- stuck-help

yes some what i do

- stuck-help

|dw:1447445361887:dw| am i on the right track

- 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

Also, yes, you're on the right track.

- stuck-help

ok so how does the pythagorean theorem play to this

- stuck-help

and where do you get the 4 and 8 squared and 3 and 6 squared

- malcolmmcswain

https://learnzillion.com/lesson_plans/6406-find-the-length-of-a-line-segment-on-the-coordinate-plane-using-the-pythagorean-theorem

- stuck-help

ok so do we do thins for both lines

- stuck-help

ok so i got the 4 and 8 squared

- stuck-help

@malcolmmcswain one thing has got me confused

- stuck-help

##### 1 Attachment

- malcolmmcswain

Ok, so that's just for finding the scale.

- malcolmmcswain

It's comparing them as a ratio to see how much we decreased.

- 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

Yeah, that's right. He made a mistake.

- stuck-help

and how do you get 3 and 4 becasue im getting 6 and 8
so 3/4

- malcolmmcswain

6/8 simplifies to 3/4

- stuck-help

oh ok not sure who i should metal here both of you were big help thank you so much

- malcolmmcswain

No problem. If anybody, medal lochana. I don't need a medal, and he really deserves it.

- 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

Happy to help! ^-^

Looking for something else?

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