Answer: The correct option is
(D) rotation of 270 degrees counterclockwise and shifting 3 units up.
Step-by-step explanation: We are given to select the correct transformations that were applied to triangle ABC to obtain triangle A'B'C'.
From the graph, we note that
the co-ordinates of the vertices of triangle ABC are A(3, 4). B(5, 6) and C(8, 1).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(4, 0), B'(6, -2) and C'(1, -5).
We see that
if a point (x, y) is rotated 270 degrees counterclockwise and then shifted 3 units up, then its co-ordinates becomes
(x, y) ⇒ (y, -x+3).
With this transformation rule,
A(3, 4) ⇒ (4, -3+3) = (4, 0),
B(5, 6) ⇒ (6, -5+3) = (6, -2)
and
C(8, 1) ⇒ (1, -8+3) = (1, -5).
Since the resulting co-ordinates are the vertices of triangle A'B'C', so the required transformations rare
rotation of 270 degrees counterclockwise and shifting 3 units up.
Option (D) is CORRECT.
