Given the square below with the listed vertices, first formulate a transformatio

Question

Given the square below with the listed vertices, first formulate a transformation matrix that scales it to make two times larger in both dimensions. Next apply the transformation matrix to each vertex. Show the new position of each vertex.
Vertex A (50, 50)
Vertex B (90, 50)
Vertex C (90, 90)
Vertex D(50, 90)
Use the following to calculate the new position of each vertex:
[X New Pos
Y New Pos
1] = [dx 0 0
0 dy 0
0 0 1)] [ X Old Pos
Y Old Pos
1]
Where dx = value to scale by in x dimension
Where dy = value to scale by in y dimension

Explanation / Answer

transformation matrix =T= 2 0 0 0 ........................... .. 2 0 0 0 vertex matrix V= 50 50 ....................90 50 .....................90 90 .....................50 90 hence VT gives the required matrix dx=2 ; dy =2 hence new vertex matrix = 100 100 180 100 180 180 100 180

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