Answer:
- (x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin
- (x, y) ⇒ (x +3, y +1) . . . translation 3 right a 1 up
Explanation:
You want a sequence of transformations that maps ∆ABC to ∆A'B'C' where the vertices are A(-5, 3), B(-2, 3), C(-4, 1), A'(8, -2), B'(5, -2), and C'(7, 0).
Orientation and scaling
Segment AB is a 3-unit line segment directed to the right. Segment A'B' is a 3-unit line segment directed to the left. This means there is no dilation involved in the transformation. At least, the figure has been reflected left-to-right.
Point C is below segment AB, while point C' is above segment A'B'. This means the figure has also been reflected top-to-bottom.
Together these reflections can be accomplished by either of reflection across the origin, or rotation 180° about the origin.
Translation
The reflected figure would leave A' at (5, -3). Its location at (8, -2) means the figure has also been translated to the right and up.
Translation to the right has been by 8 -5 = 3 units.
Translation up has been by -2 -(-3) = 1 unit.
(a) Description of transformations
Triangle ABC can be transformed to triangle A'B'C' by ...
- reflection across the origin
- translation 3 units right and 1 unit up
(b) Transformation rules
The corresponding ordered-pair rules for these transformations are ...
- reflection: (x, y) ⇒ (-x, -y)
- translation: (x, y) ⇒ (x +3, y +1)
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Additional comment
The single transformation that will accomplish the mapping is ...
(x, y) ⇒ (3 -x, 1 -y) . . . . . reflection across the point (3/2, 1/2)