Question

On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, negative 2), B (1, negative 2), C (2, negative 5), and D (negative 2, negative 5). The second trapezoid has points A prime (negative 4, negative 1), B prime (negative 2, negative 1), C prime (negative 1, negative 4), and D prime (negative 5, negative 4).
Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.

The rule for the translation can be written as T–3, 1(x, y).
The rule for the translation can be written as T–1, 3(x, y).
The rule for the translation can be written as
(x, y) → (x + 1, y – 3).
The rule for the translation can be written as
(x, y) → (x – 3, y + 1).
Trapezoid ABCD has been translated 3 units to the right and 1 unit up.

Answer 1

True statements:
- The rule for the translation can be written as T–3, 1(x, y).
- The rule for the translation can be written as (x, y) → (x – 3, y + 1).

Reason: each vertex moves from (x,y) to (x−3, y+1) (e.g., A(−1,−2) → A'(−4,−1)), so the translation vector is (−3,1).