Question

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

Answer 1

Let X and Y be the respective new co ordinates so,

According to the question ,
The coordinate system is shifted up by 5 units so,
this means that the values at 0 will be shifted to 5 , 1 to 6..
So the shift is
y=Y+5
So Y=y-5

Now the coordinate system is also shifted in x direction by 3 units to left so,
x=X-3
X=x+3
So, the coordinates to represent any line, point, graph on the  system was
(x,y)
After the respective shifts the new coordinates that should be used are
(x+3,y-5)

(Note that even if x shift is performed first then the y shift even then it will yield the same result)

Answer 2

Given:

The rectangle coordinates shifted

"5 units to the up"

"3 units to the left"

To find:

Describe the translation

Solution:

The coordinate system of a rectangle is shifted up to "5 units"

Then the values at "0 is shifted to 5", "1 to 6".

Then the shift value is

y = Y + 5

So Y = y - 5

Then the coordinate system gets shifted in x direction by "3 units to the left"

x = X - 3

X = x + 3

After the respective shifts, the new coordinates that should be used are

(X, Y)

( x + 3, y - 5 )