The rigid transformation formula applied on triangle ABC is translation formula T(x, y) = (6, 4). (Correct choice: C)
How to determine the rigid transformation between a figure and its image
In this problem we must determine the rigid transformation between a figure and its image. We notice that triangle ABC becomes triangle DEF by means of a translation process, whose definition is introduced below:
- Horizontal translation: 6 units right.
- Vertical translation: 4 units up.
Translation is defined by following operation:
P'(x, y) = P(x, y) + T(x, y)
Where:
- P(x, y) - Original point.
- P'(x, y) - Resulting point.
- T(x, y) - Vector translation.
Vector translation: T(x, y) = (6, 4)
If we know that A(x, y) = (- 4, - 2), B(x, y) = (- 2, - 3) and C(x, y) = (- 4, - 3), then vertices of triangle DEF are, respectively:
D(x, y) = (- 4, - 2) + (6, 4)
D(x, y) = (2, 2)
E(x, y) = (- 2, - 3) + (6, 4)
E(x, y) = (4, 1)
F(x, y) = (- 4, - 3) + (6, 4)
F(x, y) = (2, 1)