To transform trapezoid ABCD to create triangle A՚B՚C՚D՚, we need to apply the given transformations to each vertex of the trapezoid:
a (x, y) → (-x, -y):
- The x-coordinate becomes the negation of the original x-coordinate.
- The y-coordinate becomes the negation of the original y-coordinate.
So, vertex A (a) transforms to A՚ (-x, -y).
b (x, y) → (-y -x):
- The x-coordinate becomes the negation of the sum of the original x and y coordinates.
- The y-coordinate remains the same.
So, vertex B (b) transforms to B՚ (-y -x, y).
c (x, y) → (x, -y):
- The x-coordinate remains the same.
- The y-coordinate becomes the negation of the original y-coordinate.
So, vertex C (c) transforms to C՚ (x, -y).
d (x, y) → (-x, y):
- The x-coordinate becomes the negation of the original x-coordinate.
- The y-coordinate remains the same.
So, vertex D (d) transforms to D՚ (-x, y).
Therefore, the resulting triangle A՚B՚C՚D՚ is formed by the transformed vertices A՚ (-x, -y), B՚ (-y -x, y), C՚ (x, -y), and D՚ (-x, y).
Trapezoid ABCD was transformed to create triangle A՚B՚C՚D՚.
a (x, y) → (-x, -y)
b (x, y) → (-y -x)
c (x, y) → (x, -y)
d (x, y) → (-x, y)
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