Answer:
Option D. is the correct transformation.
Step-by-step explanation:
Coordinates of the given points are R(0, 0), S(-2, 3) and T(-3, 1)
Coordinates of the new points after transformations are R'(2, 0), S'(0, -3) and T'(-1, -1).
Option A.
Rule for 90 degree clockwise rotation about the origin and translation 2 units left is,
(x, y) → (y - 2, -x)
This rule is not applicable for the given transformation.
Option B.
a 90° counterclockwise rotation about the origin and then a translation 2 units right
Rule → (x, y) → (-y + 2, x)
This rule is not applicable for the given transformation.
Option C.
A translation 2 units left and then a reflection over the y axis.
Rule → (x, y) → (-x + 2, y)
This rule is not applicable for the given transformation.
Option D.
A translation 2 units right and then a reflection over the x axis.
Rule → (x, y) → (x + 2, -y)
R(0, 0) → (2, 0)
S(-2, 3) → (0, -3)
T(-3, 1) → (-1, -1)
Option D. is the correct transformation.
