Question

On a coordinate plane, 2 trapezoids are shown. Trapezoid 1 has points A (negative 4, 3), B (1, 3), C (0, 0), and D (negative 3, 0). Trapezoid 2 has points A prime (negative 1, 1), B prime (4, 1), C prime (3, negative 2), and D prime (0, negative 2).

Answer 1

Trapezoid 2 is the image of Trapezoid 1 under the translation by vector <3, −2>.

Check on the vertices:
- A(−4, 3) → A′(−4+3, 3−2) = (−1, 1)
- B(1, 3) → B′(1+3, 3−2) = (4, 1)
- C(0, 0) → C′(0+3, 0−2) = (3, −2)
- D(−3, 0) → D′(−3+3, 0−2) = (0, −2)

Mapping rule: (x, y) → (x + 3, y − 2). This translation preserves lengths and orientation.