Answer: Â The required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
Step-by-step explanation:  We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
From the figure, we note that
the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).
We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :
(x, y)  ⇒  (-y, x).
That is
A(0, 4)  ⇒  (-4, 0),
B(0, 0)  ⇒ (0, 0),
C(2, 3)   ⇒ (-3, 2).
Now, if the vertices of the rotated triangle are translated  2 units right and 3 units down, then
(x, y)  ⇒  (x+2, y-3).
That is, the final co-ordinates after rotation and translation will be
(-4, 0)  ⇒  (-4+2, 0-3) = (-2, -3),
(0, 0)  ⇒ (0+2, 0-3) = (2, -3),
(-3, 2)  ⇒ (-3+2, 2-3) = (-1, -1).
We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
