Given the vertices of triangle A:
A(-2, 4), (-2, 2), (-4, 2)
Vertices of triangle B:
B(3, -1), (3, -3), (1, -3)
Let's find the rule to describe the transformation that occured to obtain triangle B from triangle A.
To find the transformation rule subtract the vertices of traingle A form the corresponding vertices of triangle B.
We have:
(3 - - 2, -1 - 4) ==> (3 + 2, -1 -4) ==> (5, -5)
(3 - - 2, -3 -2) ==> (3 + 2, -3 - 2) ==> (5, -5)
(1 - - 4, -3 - 2) ==> (1 + 4, -3 - 2) ==> (5, -5)
From the figure given, we can see triangle A moved 5 units to the right and down 5 units to obtain triangle B.
The form of transformation that occured here is called translation.
A translation 5 units right is written as: x + 5
A translation 5 units down is written as: y - 5
Triangle A was translated 5 units to the right and 5 units downwards to obtain triangle B.
Using the rules of translation, the rule to describe the transformation is:
(x, y) ==> (x + 5, y - 5)
ANSWER:
(x, y) ==> (x + 5, y - 5)