The transformation from figure 1 to figure 2 is shown on the graph.
It is required to choose from the options the composition of transformation that maps figure 1 onto figure 2.
The coordinates of the vertices of figure 1 are (5,2), (5,7), and (8,5).
The coordinates of the vertices of figure 2 are (-2,2), (-7,3), and (-5,5).
Recall the coordinate rule of 90º counterclockwise rotation about the origin:
[tex](x,y)\rightarrow(-y,x)[/tex]Hence, the rotation of figure 1 90º counterclockwise gives the vertices:
[tex](-2,5),(-7,5),(-5,8)[/tex]Translate the image 3 units down by subtracting 3 from the y-coordinates to give vertices:
[tex]\begin{gathered} (-2,2),(-7,2),(-5,5) \\ \end{gathered}[/tex]Notice that these vertices match that of figure 2.
It follows that the sequence of transformation is 90ºcounterclockwise rotation about the origin, followed by a translation three units down.
The answer is B followed by D.