Question

Which sequence of rigid transformations will not map the preimage ΔABC onto the image ΔA′B′C′ ?

a reflection across the y-axis followed by a reflection across the x-axis



a rotation 90° clockwise about the origin followed by a reflection across the x-axis



a rotation 180° clockwise about the origin followed by a reflection across the line y = -x



a reflection across the line y = x

Answer 1

A reflection across the y axis then across the x axis is the only option that does not work

Answer 2

The correct options are 2 and 4.

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.