<u><em>Option 4 is not a rigid transformation.</em></u>
In mathematics, transformation could be;
Rigid Transformation; This includes reflection, rotation, translation.
Non - Rigid Transformation; This includes dilation and shear.
Now, a transformation is said to be a rigid transformation when the newly transformed image retains the same shape and size as it was before it was transformed. Although it can change position.
Whereas, it is termed non - rigid transformation if the shape or size changes.
Let us look at the triangles in the option;
Option 1; In this option, we see that the two triangles maintain the same shape and size and thus the transformation is rigid.
Option 2; In this option, we see that the two triangles maintain the same shape and size and thus the transformation is rigid.
Option 3; Similar to options 1 & 2, we see that the two triangles maintain the same shape and size and thus the transformation is rigid.
Option 4; We see that one of the triangles is bigger than the other. Since the transformed triangle is not the same size as it was before transformation, then it is not a rigid transformation.
Sin is equal to the same number, no matter how big or small you make the triangle because the sine of the angle is equal to the opposite side divided by the hypotenuse.
