use a composition of a horizontal and vertical translation to write the translation t(-5, 2,) (x,y)
(-5,2) = (-5,0) + (0,2)
To perform a composition of a horizontal and vertical translation, you need to apply the horizontal translation first followed by the vertical translation.
A horizontal translation shifts all points left or right, while a vertical translation shifts all points up or down.
Let's start with the horizontal translation. The horizontal translation t(a, 0) moves each point (x, y) horizontally by 'a' units. So to perform the horizontal translation t(-5, 0), you will move each point 5 units to the left.
Now, let's move on to the vertical translation. The vertical translation t(0, b) moves each point (x, y) vertically by 'b' units. Applying the vertical translation t(0, 2) will shift each point 2 units up.
Now, when you perform both translations, you first apply the horizontal translation t(-5, 0) by moving each point 5 units to the left, and then apply the vertical translation t(0, 2) by shifting each point 2 units up.
So, the composition of the horizontal and vertical translation t(-5, 2) applied to a point (x, y) is:
(x, y) -> (x - 5, y + 2)