Negative & Positive Shear Factor

[sorter]

My question relates to constructional geometry & matrices aren't to be involved in the solution because stated Math level is up to O Levels... The figure below shows shear with y=3 as invariant line & shear-factor of 3

My question is if you are provided the original polygon & asked to do shear with y=3 as invariant & shear-factor 3 or -3 how would I know whether to slide segment AD to right or left? Same confusion thus occurs with segment BC?

Moreover shear-factor is defined via (object-image dist)/(object-invariant dist) thus if the object polygon ABCD & its image say the red one is given & you are asked to completely define the transformation I can give the invariant line & the factor's magnitude but I can't tell the sign (+ or -) of the shear-factor because distances are always positive? Plz help this teacher

 

[pat_connell]

in understanding the concept.In order to determine whether to slide segment AD to the right or left, you will need to look at the original polygon and determine if segment AD is above or below the invariant line. If it is above the line, you will slide it to the right with a shear-factor of 3. If it is below the line, you will slide it to the left with a shear-factor of -3. The same applies for segment BC.When determining the shear-factor, you can use the formula (object-image dist)/(object-invariant dist) to calculate the magnitude of the shear-factor. However, in order to determine the sign of the shear-factor (positive or negative), you will need to look at the direction of the transformation. If the object is moving in the same direction as the invariant line, the shear-factor is positive. If the object is moving in the opposite direction as the invariant line, the shear-factor is negative.