Geometrical Transformations

[abcde]

When do we get a negative shear factor? :? :?

 

[Nibz]

When do we get a negative shear factor? :? :?

When the points are below the invariant line or in negative axes..

 

[abcde]

As far as i have observed; when the x-axis is invariant, negative shear factor is obtained when the image is to the left of the object. with the y-axis invariant a negative shear factor is obtained when the image is below the object. Is this correct?

 

[Nibz]

Not the image but the invariant line!
=> when the invariant line is the "x-axis".. shear for the points on the left of this line is negative (right of the inv. +ive)
=> when the invariant line is the "y-axis".. shear for the points below this line is negative (above this line +ive)
POSITIVE SHEAR = GO TOWARDS RIGHT/UP
NEGATIVE SHEAR = GO TOWARDS LEFT/DOWN

 

[abcde]

got it. POSITIVE SHEAR: GO TOWARDS RIGHT/GO UP.
NEGATIVE SHEAR: GO LEFT/DOWN. AS THE CASE MAY BE...

 

[Nibz]

^ EXACTLY!!

 

[XPFMember]

When do we get a negative shear factor? :? :?

Assalamoalaikum!!

Formula for shear factor => dist. point moves due to shear/dist. of that point from invariant line

dist. point moves due to shear : always move from object to image now see if it is +ve or -ve (+ve is up or right movement and -ve is down or left movement)

dist. of that point from invariant line:always move from invariant line to the point now check whether its positive or negative then use calc. to find out final ans. putting signs appropriately

The same applies for stretch dont forget to go from invariant line to point

so all u do is to note how to move and then notice the directions and hence put signs accordingly

is it ok now ??