Question

Can someone please help me transform a quadrilateral using the rule (x-2,y+8) i'm a little confused on what i'm doing please help me

Answer 1

the point's are A(-2,2) B(-2,4) and D (2,2) and I have to transform them using the rule (x-2,y+8) Do i just add those to the points? this is a little confusing for me i'm sorry

Answer 2

I tried doing it i'm just not sure if im doing it correctly for point A (-2,2) would I just multiply -2 by -2 and then 2 times 8 to get the new coordinates or am i looking at this all wrong?

Answer 3

so, your first point is A(-2,2). The transformation rule is (x-2,y+8). This means you take the x-value for the point (-2 here), and you subtract 2 (-2-2 = -4). Then you take the y-value for the point (2 here), and you add 8 (2+8 = 10). The new coordinate is (-4,10). Repeat for all the other points.

Answer 4

Thank you for explaining that for me can you please stay while I tr a new point to make sure i'm doing it correctly I shouldn't take that long

Answer 5

Okay I did B(-2,4) I think I added/subtracted the right things I first did -2--4=-6 and then I did 4+8=10 so the new coordinate would be (-6,12) did I do that right?

Answer 6

Point B(-2,4). What is the x value? What is the y-value?

Answer 7

-2 is the X value and 4 is the Y value

Answer 8

Okay. The rule is the new x value is the old x value - 2: (x-2,y-8)
What is the new x value going to be?

Answer 9

-4?

Answer 10

As an old math teacher of mine liked to say, "is that an answer, or a prayer?" :-)

Answer 11

an answer lol(: I'm sorry I just second guess myself a lot

Answer 12

-2 - 2 = -4. Correct!

Answer 13

Now, the part of the rule for the y value is y - 8. What will the new y value be?

Answer 14

err, sorry, the rule for the y value is y + 8, I copied it wrong earlier

Answer 15

Oh okay so I add it together I would get 12

Answer 16

right. so the newly transformed point B is where?

Answer 17

(-4,12)(:

Answer 18

you got it. make sense now? the transformation rule is just a little recipe for how to make the new point. do the rest of them and I'll check them for you.

Answer 19

in this case, the rule could be read as "move left 2 points and up 8"

Answer 20

Thank you so much this makes so much more sense and thank you for being willing to check the rest I realized I forgot to put C(2,4) so i'm going to figure that out right now and I will tell you

Answer 21

Okay so now that I understand it now its a lot easier to do for C(2,4) I just subtract 2 and 2 so I would get 0 and for 4 I just add 4+8 getting 12 so the new coordinate is (0,12) and then for D(2,2) I subtract 2-2 and get 0 and then add 2+8 getting 10 so the answer is (0,10) hopefully I did those right(:

Answer 22

Yes, I think you did. Here's a picture of what happens: (translated points are A', B', C', D')

Answer 23

Thank you so so so much! the second part of the question ask me describe what characteristics you would find if the corresponding vertices were connected with line segments? basically by looking at your picture I can tell that it would be the shape shape just at different coordinates right?

Answer 24

this was a relatively simple, linear rule: the object stayed the same shape and size, and just moved to a different spot.

Answer 25

That's what I was thinking by looking at your picture thank you very much you helped me out a lot(:

Answer 26

now, with a different rule, we can do lots of interesting things. For example, if we multiply instead of adding, we'll expand or contract the figure. If the two halves of the rule aren't identical, the expansion/contraction won't be, either. Say we have a box at (0,0), (0,1), (1,1), (1,0). if the rule is (2x,2y) the new box becomes (0,0), (0,2), (2,2), (2,0). that's just scaling it up by a factor of two in each direction. What if we had a rule that was (2x,3y)? Then the box would become (0,0), (0,3), (2,3), (2,0). Now our square box is a rectangle 3 units high and only 2 units wide.

For even more mind-bending, consider that you could have a rule like (y, x). In other words, we swap the values of x and y to get the new point. What would that do to your original picture?

Answer 27

It's crazy there's so many options that change everything! If you had it as (y,x) wouldn't it swap the figure it would kind of be backwards.. I can see it in my head lol I just don't know how to describe it

Answer 28

it reflects it across a diagonal line running through the origin (at 45 degrees)

Answer 29

you're really good at this seriously all this makes a lot more sense now that you're explaining it to me

Answer 30

if we had a curve we could describe with a function, instead of a set of points like this (which are not a function because a vertical line sometimes crosses the figure more than once), we could write these transformations in a different way. Remember how I said the first rule was equivalent to "left 2 and up 8"?

if we have a function y = f(x), we can do that same thing:

g(x) = f(x+2) + 8

g(x) is a copy of f(x), shifted 2 units to the left, and 8 units up.

Answer 31

it's a little confusing at first why we add 2 instead of subtracting 2, but we don't need to go into that right now unless you're really curious :-)

Answer 32

I would love to go into it because it sounds interesting but first I have to do the rest of my homework maybe later on today if you're logged in I will talk to you more about it if that's okay(:

Answer 33

okay, I'll be in and out, but will have a look for you. shoot me a message when you have a question, and I'll respond the next time on I'm the site.

Answer 34

you'll see this stuff later in your math classes, I'm sure. you can help all of your friends at that point :-)

Answer 35

Thank you very much I will make sure to message you!