Write a function that determines whether a given 3\times 3 matrix qualifies as a composite transformation matrix (CTM) in 2 D graphics.
Using only the geometric interpretation of the determinant, explain why the determinant of the Jacobian matrix |JI| is equal to -1 for a reflection transformation.
3. State and clearly formulate the three essential geometric properties of 2D determinants with respect to transformations:
(a) Scaling
(b) Shearing
(c) Distributivity
4. Let matrix A be a 3\times 3 matrix representing a transformation:
A=[[0,-1,0],[1,0,0],[0,0,1]]
(a) Identify the transformation represented by A.
(b) What happens to the point (3,-1) after applying this transformation?
5. Suppose a triangle has vertices at A(2,2),B(3,3),C(6,1). Perform a reflection of this triangle about the line y=x. Give the new coordinates of all vertices.
6. Consider a scaling matrix that scales by a factor of 2 in the x-direction and 0.5 in the y-direction with respect to the origin.
(a) Write the matrix for this transformation.
(b) Apply this transformation to the point P(-4,2) and provide the new coordinates.
