The series of transformations from the given points to the corresponding transformed points are:
A(1, -1) to A'(7, 1): Horizontal shift 6, Vertical shift 2
B(3, -1) to B'(7, 3): Horizontal shift 4, Vertical shift 0
C(3, -4) to C'(4, 3): Horizontal shift 1, Vertical shift -1
D(2, -3) to D'(5, 2): Horizontal shift 3, Vertical shift 1
E(1, -4) to E'(4, 1): Horizontal shift 3, Vertical shift -3
How too determine the series of transformations?
There are different types of transformations such as:
Translation
Rotation
Dilation
Reflection
Now, the coordinates of the polygon before transformation are:
A(1, -1)
B(3, -1)
C(3, -4)
D(2, -3)
E(1, -4)
The final coordinates after transformation are:
A'(-7, 1)
B'(-7, 3)
C'(-4, 3)
D'(-5, 2)
E'(-4, 1)
To find the series of transformations from point A(1, -1) to point A'(7, 1) and from point B(3, -1) to point B'(7, 3), we can analyze the given points and their transformations:
Point A(1, -1) is transformed to point A'(7, 1) using the following transformations:
Horizontal shift: 7 - 1 = 6
Vertical shift: 1 + 1 = 2
Point B(3, -1) is transformed to point B'(7, 3) using the following transformations:
Horizontal shift: 7 - 3 = 4
Vertical shift: -1 + 1 = 0
Point C(3, -4) is transformed to point C'(4, 3) using the following transformations:
Horizontal shift: 4 - 3 = 1
Vertical shift: -4 + 3 = -1
Point D(2, -3) is transformed to point D'(5, 2) using the following transformations:
Horizontal shift: 5 - 2 = 3
Vertical shift: -3 + 2 = 1
Point E(1, -4) is transformed to point E'(4, 1) using the following transformations:
Horizontal shift: 4 - 1 = 3
Vertical shift: -4 + 1 = -3