A'b'c'd' is the image of abcd . what transformation(s) would result in this image?

1. abcd is reflected over the line y = x .
2. abcd is dilated about the origin with a scale factor of -1.
3. abcd is reflected across the y-axis and then the x-axis.
4. abcd is rotated 180° around the origin.

Option 3 and 4.

Step-by-step explanation:

From the given figure it is clear that the vertices of figure ABCD are A(3,-2), B(5,-5), C(3,-5) and D(2,-4).

The vertices of figure A'B'C'D' are A'(-3,2),B'(-5,5), C'(-3,5) and D'(-2,4).

The relation between preimage are image is

It means ABCD is rotated 180° around the origin.

If ABCD is reflected across the y-axis and then the x-axis.

Across the y-axis :

Across the x-axis :

Across the y-axis and then the x-axis : .

Therefore, the correct options are 3 and 4.