Answer:
The correct option is D.
Step-by-step explanation:
It is given that the after transformation figure ABCD onto HGFE. It means HGFE is image of ABCD after transformation.
From the figure it is noticed that A(2,-1) and H(-6,1).
Rotation of 90 degree clockwise about the origin followed by the reflection across the x-axis is expressed as
[tex](x,y)\rightarrow (y,-x)\rightarrow (y,x)[/tex]
Therefore the image of A(2,-1) is (-1,2), which are not the coordinates of H. Option A is incorrect.
Translation 3 unit up followed by the reflection across the y-axis is expressed as
[tex](x,y)\rightarrow (x,y+3)\rightarrow (-x,y+3)[/tex]
Therefore the image of A(2,-1) is (-2,2), which are not the coordinates of H. Option B is incorrect.
Reflection across the x-axis followed by rotation of 90 degree counterclockwise about the origin is expressed as
[tex](x,y)\rightarrow (x,-y)\rightarrow (y,x)[/tex]
Therefore the image of A(2,-1) is (-1,2), which are not the coordinates of H. Option C is incorrect.
Translation 8 unit left followed by reflection across the x-axis is expressed as
[tex](x,y)\rightarrow (x-8,y)\rightarrow (x-8,-y)[/tex]
Therefore the image of A(2,-1) is (-6,1), which are the coordinates of H. Option D is correct.
