The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:
1) Translation (x, y) → (x + 8, y + 2)
2) Reflection across the x-axis (x, y) → (x, -y)
So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.
What are the transformation rules?
The transformation rules are:
- Reflection across x-axis: (x, y) → (x, -y)
- Reflection across y-axis: (x, y) → (-x, y)
- Translation: (x, y) → (x + a, y + b)
- Dilation: (x, y) → (kx, ky)
Calculation:
The pentagons in the graph have vertices as
For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)
For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)
Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".
Applying the Translation rule for the pentagon ABCDE:
The rule is (x, y) → (x + a, y + b)
So, the variation is
-4 + a = 4
⇒ a = 4 + 4 = 8
5 + b = 7
⇒ b = 7 - 5 = 2
So, the pentagon ABCDE is translated by (x + 8, y + 2).
Applying the Reflection rule for the translated pentagon:
The translated pentagon has vertices (x + 8, y + 2).
When applying the reflection across the x-axis,
(x + 8, y + 2) → {(x + 8), -(y + 2)}
Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}
Verification:
A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"
B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"
C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"
D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"
E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"
Learn more about transformation rules here:
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