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6.1. An affine transformation of plane is given by the formulas 
.
Find images of: a) points 
; b) lines 
.
6.2. An affine transformation of plane is given by the formulas 
. Find pre-images of: a) points 
; b) lines 
.
6.3. Write formulas determining an affine transformation of plane transferring the points 
to 
respectively: 
.
6.4. Find all fixed (immovable) points of the following affine transformation given by formulas:
a) 
; b) 
.
6.5. Write the formulas determining the products 
and 
of the following affine transformations: 
.
6.6. Write the formulas determining the inverse transformation for 
if there is such a transformation.
6.7. Let an affine transformation 
be given. Compose an equation of the image of the following curve: a) 
; b) 
.
6.8. Let an affine transformation 
be given. Compose an equation of the pre-image of the following curve: a) 
; b) 
.
6.9. Write formulas determining an affine transformation transferring the lines 
, 
to the lines 
respectively, and the point 
to the point 
.
6.10. Find all possible affine transformations of plane transferring the points to respectively: 
, if such transformations exist.
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| Orthogonal transformations of plane | | | Exercises for Homework 6 |