What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle transformed formed by ordered pairs A prime at negative 4, negative 2, B prime at negative 4, negative 1, C prime at negative 1, negative 1, D prime at negative 1, negative 2. Reflected over the x-axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x-axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise

Reflection over the y-axis and rotation of 180°

Step-by-step explanation:

We have,

Rectangle ABCD with co-ordinates A (-4,2), B (-4,1), C (-1,1) and D (-1,2).

It is transformed to a new rectangle A'B'C'D' with co-ordinates A' (-4,-2), B' (-4,-1), C' (-1,-1) and D' (-1,-2).

The graph of both the triangles is shown below.

We see that,

The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

Reflected about y-axis Rotation of 180°

A = (-4,2) (4,2) A' = (-4,-2)

B = (-4,1) (4,1) B' = (-4,-1)

C = (-1,1) (1,1) C' = (-1,-1)

D = (-1,2) (1,2) D' = (-1,-2)

Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.