The vertices of a trapezoid are shown below.
(0, 8), (6, 16), (6, 12), (0, 16)
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2 ?
A.
(2, 18)
B.
(12, 24)
C.
(0, 4)
D.
(4, 3)

- rayman5766

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- rayman5766

can any one help me

- rayman5766

@Nnesha hey are you get with math becaues i need your help if you are

- rayman5766

hey mathmate can you helpme wit this problem

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## More answers

- mathmate

@rayman5766
If you want help, please proof-read your post.
Casually copied and pasted posts discourage helpers.

- rayman5766

oops sorry bot that its 1/2

- rayman5766

i for got to typed that in hold on

- mathmate

Are you familiar with dilations?

- rayman5766

yes

- mathmate

A dilation with a factor of 1/2 will make the figure bigger or smaller?

- rayman5766

bogger i would hope

- mathmate

A dilation factor of 2 will make the figure twice as big as the original,
a dilation factor of 3 will make the figure three times as big as the original,
So rethink for a factor of 1/2!

- rayman5766

oh i think i see so the figure would be smaller i guess

- mathmate

So do we agree that a scale factor of more than one will make the image bigger, and a scale factor of less than one will shrink the image (even it's called dilation).

- rayman5766

yes we can

- mathmate

Good!
So a factor of 1/2 will shrink the original to what size?
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?

- rayman5766

1,4?

- mathmate

Please explain how you arrived at (1,4).

- mathmate

Remember that 1/2 means \(\frac{1}{2}\), or 0.5.

- rayman5766

actual would it be 1,1

- mathmate

Please explain how you arrived at (1,1).

- mathmate

(note: I will ask you to explain even if the answer is correct!)

- mathmate

(note: I will ask you to explain even if the answer is correct, so stop guessing)

- rayman5766

sorry i was using multiplication for my answers but that would make more sens 1/2 is 50 so in dilation it would be 0,5 sorry for my stupidity

- mathmate

So please explain how you got (1,1).

- rayman5766

well i thought i seen a pattern with the 2,4 being 4 2x2 would be 4 and 3 x 2=6

- rayman5766

so i thought 1 would equal 1.1 but i forgot it was a 1/2 wich would make it 0.5 sorry i think of some other thing wich would make it the answer

- rayman5766

also i keep putting wich and now which

- mathmate

Good, the fact is that each of the (x,y) coordinates must be multiplied by the scale factor.
For example, if we apply a factor of 1.5 to P(2,5), we would get P'(2*1.5, 5*1.5)=P'(3,7.5).
So can you try again?

- rayman5766

i meant not

- rayman5766

ok i can try

- mathmate

Not a problem unless you order a sandwhich at a restaurant! lol

- rayman5766

ha good one you see when i think of math i think of possibility's so i think of this which would make that

- rayman5766

be the answer

- mathmate

Just in case our original question was lost:
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?

- rayman5766

so i get confused and make a dump aswer which makes me look like an idiot

- mathmate

The only dumb answer is the one that was never made!

- rayman5766

2*1.2 and 3*1.5 =

- rayman5766

i didn't put the answer becaues i am trying to make sure i am going in the right path here so am

- rayman5766

wait would my answer be A

- mathmate

The answer to \(my\) question, P(1,2) with a factor of 0.5 is
P'(1*0.5, 2*0.5) = P'(0.5,1)
(use a calculator if you need to)
Understand how the above problem was solved before thinking about the problem you are trying to solve.
Math is about understanding. We should always understand how to solve a class of problems BEFORE attempting exercises on the topic. Guessing will only make math hard, for now and for the future.

- rayman5766

wow that was some hard core wisdom you just said but you are correct

- rayman5766

also that would make sens knowing 1/5 is 0.5 oki thik i get it

- mathmate

1/2 = 0.5, 1/5\(\ne\) 0.5

- rayman5766

oh sorry i know that

- rayman5766

i put a 5 and not a 2my bad

- rayman5766

but one more thing were does the 3 you put up there come from '

- mathmate

Just in case our original question was lost:
For example, you have a point P(1,2).
Dilation factor of 2 will bring it to P'(2,4).
Dilation factor of 3 will bring P'(3,6).
What would be the coordinates of P' using a dilation factor of 1/2?
If this is what you meant, they were examples

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