Translation refers to a rigid motion or transformation where you move an object from one location to another.
Translations are defined by the rule (x,y) -- (x+a, y+b) where the words right and left represent a change in the x-axis, and the words up and down a change in the y-axis.
In this exercise are given the coordinates of the vertices of the triangle ABC, which are (1,3), (4,5), and (3,1) respectively. It is asked to find the coordinates of the new triangle, A'B'C', after a translation produced by the rule (x,y)-- (x+1,y-2).
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A(1,3) ---- (1+1,3-2) ---- A'(2,1)
B(4,5) ---- (4+1,5-2) ---- B'(5,3)
C(3,1) ---- (3+1,1-2) ---- C'(4,-1)
The coordinates of the triangle after the translation are A'(2,1), B'(5,3), and C'(4,-1)
