Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV, as shown below:
What will be the location of U' in the image trapezoid S'T'U'V'?
A. (16, −2)
B. (14, −2)
C. (14, 1)
D. (16, 1)

- anonymous

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- anonymous

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- anonymous

@calculusxy @phi @peachpi

- phi

pick a point on rectangle JKLM, say point J which is at (-5,1)
where is point J' ?

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## More answers

- anonymous

In my opinion is A, but im not sure i just need an explanation

- phi

say point J which is at (-5,1) where is point J' ?
can you find point J' and "read off" its (x,y) coordinates?

- anonymous

Point J is at 4,5

- phi

point J prime J'
yes, it is at x=4
what is its y ? (its y is not 5)

- anonymous

y is at 3? im not sure about y

- phi

how many "steps up" (or boxes) from the x-axis up to J' ?

- anonymous

3?

- phi

Here is a picture counting up 2 steps (see the red numbers?)

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- anonymous

ohhh, yes i see them

- phi

so how far up to J' ?

- anonymous

2

- phi

how far up from the x-axis? (2 gets us 1/2 way)

- anonymous

3 then, i really dont know omg

- phi

you will get it.
you put your finger on the x-axis below J' and count up 1,2,etc
until you are at J' (the corner of the rectangle)

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- anonymous

5

- phi

like this

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- anonymous

ohhh i get it now

- phi

the corner of the box (labeled J') is at (4,4)
from the "origin" you move sideways 4 steps, then 4 steps straight up.

- phi

so J at (-5,1) moved to J' at (4,4)
what do we add to -5 to make it 4 ?
what do we add to 1 to make it 4 ?

- anonymous

1 and 3

- phi

ok on the 3 (so remember we add 3 to the y number)
but
-5+1 = -4 and we want +4

- anonymous

so what do we do? :/

- phi

the other way to figure it out is put your finger on J and count how many steps to the right until you are directly under J'
(it is more than 1 step)

- phi

when I say point J, I mean the corner of the rectangle labeled J
it is at (-5,1)

- anonymous

i dont get it, the part of counthing steps to the right

- phi

can you put your finger on the corner of the rectangle near the label J ?

- anonymous

yes

- phi

and move your finger to the right one box, then two boxes, and so on ?

- anonymous

okay i do that up to where?

- phi

keep doing that (and counting) until you are directly under the corner of the rectangle labeled J'

- anonymous

2?

- phi

|dw:1440886102612:dw|

- phi

if you count it right, it should take 5 steps to get to the y-axis.
and we still have some more steps to get to be under J

- anonymous

so its more than 5? its not A like i thought it was?

- phi

this is a complicated problem. we are trying to figure out how much they moved point J to get to J'
we see it was "slid over" so many steps. we need to figure out how far.
it is the number of steps to take us from -5 to +4

- anonymous

thats complicated

- phi

yes. do you see that if we are at J and move 2 steps will be here (see pic)

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- anonymous

yes ii see that.

- phi

we need to count how many steps from J to get to the "red 1" that is under J'

- anonymous

which J i dont get this sorry.

- phi

from the red circle to the green circle. how many steps?

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- anonymous

9

- phi

yes.
another way to find that is to do
4 - (-5) = 4+5 = 9
but the idea is we
ADD 9 to x and ADD 3 to y

- anonymous

i think it was easier counting the boxes lol

- phi

it is good to learn how to do the subtraction idea. but now we are almost ready to answer the question
What will be the location of U'
first, can you read off the (x,y) coords of point U ?

- anonymous

6 and im not sure about the y cord

- phi

we want the coordinates where the red circle is.
first , look on the x-axis. what number are we at when we are right above the red circle?

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- anonymous

7

- phi

in case you did not know, we are interested in the "corners" of the shape (not where the label is )
yes 7 over.
now how far down ? (look on the y-axis... what number is straight across to the red circle)
(or count down)

- anonymous

2? im confused there

- phi

it's -2 because we count down (from the x-axis)
(+2 would be 2 above the x-axis)

- anonymous

yes, -2 sorry.

- phi

Does this help?

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- anonymous

that helps!

- phi

if you put your finger at the "orgin" (where the x-axis and y-axis cross)
you count down 2 steps, then 7 steps to the right, and you will be at the red circle.

- phi

so we figured out that U is at (-2,7)
we now use the "rule" (from up above) if we can still remember it!
ADD 9 to x and ADD 3 to y
to find where U' is
can you do that ?

- anonymous

so i add 9 to -2 abd 3 to 7?

- phi

oops, I confused the x and y. but yes what you said, but with the correct numbers:
so we figured out that U is at (7,-2)
we now use the "rule" (from up above) if we can still remember it!
ADD 9 to x and ADD 3 to y
to find where U' is
can you do that ?

- anonymous

16 and 1

- phi

yes. so that is where U' is

- phi

(16,1)

- anonymous

so the correct answer is D

- phi

yes

- anonymous

thank you so much!

- phi

yw

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