To transform Triangle ABC by the matrix formed by the extreme vertices of a unit square, we first need to find the vertices of the unit square.
The extreme vertices of a unit square are:
1. (0,0)
2. (1,0)
3. (0,1)
4. (1,1)
Now, let's denote these vertices as A'(0,0), B'(1,0), C'(0,1), and D'(1,1).
To transform Triangle ABC by the matrix formed by these vertices, we'll use the transformation matrix:
[1 0]
[0 1]
since these vertices form a unit square, and this matrix represents a simple translation without any scaling or rotation.
Now, let's perform the transformation:
For vertex A(1,3):
A' = [1 0] * [1] = [1]
[0 1] [3] [3]
For vertex B(2,0):
B' = [1 0] * [2] = [2]
[0 1] [0] [0]
For vertex C(0,6):
C' = [1 0] * [0] = [0]
[0 1] [6] [6]
Now, the transformed triangle A'B'C' has vertices:
A'(1,3), B'(2,0), and C'(0,6).
Therefore, the transformed triangle by the matrix formed by the extreme vertices of a unit square is A'(1,3), B'(2,0), and C'(0,6). This transformation simply involves shifting the original triangle by the same amount in both x and y directions.
