Maths Notes for Shear and Stretch

Stretch

• The transformation consists of:o o • The invariant line Scale factor

For stretch, the transformation takes place perpendicular to the invariant line.

•

Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3

=

Y

4

X

Invariant line In the above example, the x-axis is the invariant line and the object lies on (1,1). Thus, =1

The scale factor is given to us as K = 3

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Maths Notes

Thus, acc. to the formula given above, (K) = 3= Di/1 Di = 3 Because, stretch moves perpendicular to the invariant line, thus, the image(X’) will be at (1,3). The same will take place if the invariant line is the y-axis instead of the xaxis. Area of image = K * Area of object shapes] [for cases involving

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Maths Notes

Shear

•

The transformation consists of:o o The invariant line Scale factor

• •

For shear, the transformation takes place parallel to the invariant line. Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3 4 X =

Y

Invariant In the above example, the invariant line is x-axis and the object lies on (1,1). line Do = 1 Scale factor(K) given to us is 2 Thus, K = => 2= Ds/1

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Maths Notes => Ds= 2 Because shear moves parallel to the invariant line, thus the image(X’) will be produced at (3,1). The same will take place if the invariant line is y-axis instead of the x-axis. Area of image = Area of object

N.B : Guys, that’s what I could possibly provide at the last moment as even I do have an exam tom. Hope these turn to be helpful to you all. It would be great idea to memorize the above matrices for easy and quick references.

Regards, @d!_†oX!© (Aditya) Student Forum

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