Question

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

Correct choices:
- 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: the image is shifted 3 units left and 1 unit up, i.e. by the vector (−3, 1). That is written T_{−3,1} and as (x,y) → (x−3,y+1). The other options describe different shifts (e.g. (x+1,y−3) is right 1 down 3, T–1,3 is left 1 up 3, and “3 units to the right and 1 unit up” would be (3,1), which is not the case).