Given:
We get points A(-6,-4), B(-2,-4), C(-6,-1), D(-2,3), E(-2,1) and F(-0.5,3) by observing the given grpah.
Consider the first option for point A(-6,-4).
[tex](x,y)\rightarrow(-y,x)[/tex]Substitute x=-6 and y=-4, we get
[tex](-6,-4)\rightarrow(-(-4),-6)[/tex][tex](-6,-4)\rightarrow(4,-6)[/tex]There is no point (4,-6) in the DEF triangle.
This is not true.
Consider the second option for point A(-6,-4).
[tex](x,y)\rightarrow(y,-x)[/tex]Substitute x=-6 and y=-4, we get
[tex](-6,-4)\rightarrow(-4,6)[/tex]There is no point (-4,6) in the DEF triangle.
This is not true.
Consider the fourth option for point A(-6,-4).
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]Substitute x=-6 and y=-4, we get
[tex](-6,-4)\rightarrow(\frac{1}{2}(-6),\frac{1}{2}(-4))[/tex][tex](-6,-4)\rightarrow(-3,-2)[/tex]There is no point (-3,-2) in the DEF triangle.
This is not true.
Consider the fifth option for point A(-6,-4).
[tex](x,y)\rightarrow(x+3,y+2)[/tex]Substitute x=-6 and y=-4, we get
[tex](-6,-4)\rightarrow(-6+3,-4+2)[/tex][tex](-6,-4)\rightarrow(-3,-2)[/tex]There is no point (-3,-2) in the DEF triangle.
This is not true.
Consider the sixth option for point A(-6,-4).
[tex](x,y)\rightarrow(2x,2y)[/tex]Substitute x=-6 and y=-4, we get
[tex](-6,-4)\rightarrow(-12,-8)[/tex]There is no point (-12,-8) in the DEF triangle.
This is not true.
Hence there is no similarity between triangle ABC and DEF.