Question

find the transformation Matrix that the square ABCD whose center is as (2,2) reduced the half of its size with center still remaining at(2,2) the coordinates of squre ABCD at A(0,0) B(0,4) C(4,4) D(4,0) find the coordinates of new squre​

Answer 1

The transformation matrix is [[0.5,1],[0,0.5]].

To reduce the square ABCD to half its size while keeping its center at (2,2), we can use a scaling matrix with a scaling factor of 0.5. The transformation matrix for scaling is given by:

[[0.5, 0],

[0, 0.5]]

However, this transformation will not keep the center of the square at (2,2). To do this, we need to translate the square back to its original position after scaling. The translation matrix for shifting the square by (2,2) is given by:

[[1, 2],

[0, 1]]

The overall transformation matrix is the product of the scaling and translation matrices:

[[0.5, 0],

[0, 0.5]] * [[1, 2],

[0, 1]] = [[0.5, 1],

[0, 0.5]]

To find the coordinates of the new square, we can apply this transformation matrix to the coordinates of the original square:

A(0,0) becomes (0.5, 1)

B(0,4) becomes (0.5, 2)

C(4,4) becomes (1.5, 2)

D(4,0) becomes (1.5, 1)

Therefore, the coordinates of the new square are:

A(0.5, 1) B(0.5, 2) C(1.5, 2) D(1.5, 1)