An urn holds 6 balls : a red ball, an orange ball, a yellow ball, a green ball, a blue ball and a purple ball, John selects one ball from the urn, and then, without replacing the first ball, he selects a second ball how many total selections are possible for John

Option D. a 180° rotation about the origin and then a translation left 8 units.

Step-by-step explanation:

See the attached figure_1

From the graph: Point A'(-12,-6) is the image of point A(4,6)

We will check which sequence of transformations is true:

A. a reflection across the y-axis and then a translation down 16 units

A(4,6) ⇒(-4,6)⇒(-4,-10)   (Wrong sequence)

B. a 90° counterclockwise rotation about the origin and then a translation down 8 units

A(4,6) ⇒(-6,4)⇒(-6,-4)    (Wrong sequence)

C. a 90° clockwise rotation about the origin and then a translation left 16 units

A(4,6) ⇒(6,-4)⇒(-10,-4)    (Wrong sequence)

D. a 180° rotation about the origin and then a translation left 8 units

A(4,6) ⇒(-4,-6)⇒(-12,-6)A'   (True sequence)

Note: the rules is the attached figure_2