When rewriting a composition as a single transformation, calculate the total steps on the x- and y-axis.
(x,y) → (x+1,y+2)
Practice makes perfect
We will start by writing the instructions as translations. The first instruction is to move the square 2 units to the right and 3 units up. Therefore, the translation could be written as follows.
(x,y) → (x+2,y+3)The next instruction is to move the square 1 unit left and 1 unit down. This means we will have to go in a negative direction on the x- and y-axis.
(x,y) → (x-1,y-1)
Now we should rewrite those two compositions as a single transformation. Therefore, we should calculate the total step we will have to take on the x- and y-axis. First we added 2 to the x-coordinate and then we subtracted 1. For the y-coordinate we added 3 and then we subtracted 1. We will calculate the total transformation for x and y:
x+2-1&=x+1
y+3-1&=y+2
Now we know the transformation for x and y. Together they form (x,y) → (x+1,y+2).
