Rhino is a softwater to draw a picture, you do not need to draw it . Just help m

Question

Rhino is a softwater to draw a picture, you do not need to draw it . Just help me to solve math part with steps , Thanks

1. Draw the following picture (or some similar design with no symmetry) in the square [0,10] x 10, 10 on the x-y plane. Use the transformation tools in Rhino to draw the result of applying the following matrices to the x-y plane in homogeneous coordinates. 1 0 0 1 0 0 1 10 0 1 0 a) 0 1 0 (b) 0 0 (c) 0 (d) -1 0 0 (e) 0 1 0 2 -4 1 1 2 1 0 0 1 0 1 0 0 1 Find matrices that convert the image above into the following images. Show your reasoning. Beware of where the origin is! (h) (e) (f) (g)

Explanation / Answer

1. dentify the cooridinates of the vertices A, B, C ...etc of the given shape.

2. If (x,y) are the standard coordinates of a point in the plane, the homogeneous coordinates of the point are given by (x,y,1).

3. To find the image of any point (x,y) , consider the matrix product of the given matrix with the column vector (x,y,1)' (' denoting the transpose of the row vector)

4.(e) represents scaling transformation

(f),(g) reflections

and (h) rotation anticlockwise by 90 degrees.

The corresponding matrices are

(e)

with a and b , the scalings along the x and y axis respectively

(f)

(h)

representing rotation by 90 degrees

a 0 0 0 b 0 0 0 1

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