Answer:
The correct options are 2 and 4.
Step-by-step explanation:
From the given figure it is noticed that the vertices of pre-image are A(-6,4), B(-4,6), C(-2,2) and the vertices of image are A'(4,-6), B'(6,-4),C'(2,-2).
The coordinate of image and preimage are in the form of (x,y) and (y,x).
Since the coordinates of y is x are interchanged, therefore the figure is reflected along the line \(y=x\).
Reflection across the y-axis followed by a reflection across the x-axis is defined as
\((x,y)\rightarrow (-x,-y)\)
Therefore option 1 is incorrect.
A rotation 90° clockwise about the origin followed by a reflection across the x-axis is defined as
\((x,y)\rightarrow (y,x)\)
A rotation 180° clockwise about the origin followed by a reflection across the line y = -x is defined as
\((x,y)\rightarrow (x,y)\)
Therefore option 3 is incorrect.
Therefore correct options are 2 and 4.
