we know that
Translations of geometric figures in the coordinate plane can be determined by translating the x- and y-coordinates of points. The translation is an isometric transformation (not changes the size of the figure)
so
vertex [tex] A(-5,1) [/tex] --------> [tex] A'(-3,2) [/tex]
Find the rule in the x-coordinate
[tex] -5+x=-3\\ x=-3+5\\ x=2 [/tex]
x--------> x+2
Find the rule in the y-coordinate
[tex] 1+y=2\\ y=2-1\\ y=1 [/tex]
y--------> y+1
The translation rule is
[tex] (x,y)------> (x+2,y+1) [/tex]
Verify vertex B
[tex] B(-2,7) [/tex]-------> [tex] (x+2,y+1) [/tex] ------> [tex] (-2+2,7+1) [/tex]--------> [tex] B'(0,8) [/tex] ------> is ok
Verify vertex C
[tex] C(0,1) [/tex]-------> [tex] (x+2,y+1) [/tex] ------> [tex] (0+2,1+1) [/tex]--------> [tex] C'(2,2) [/tex] ------> is ok
The three vertices have the same rule, therefore the triangles are congruent
the answer is
The translation rule is
[tex] (x,y)------> (x+2,y+1) [/tex]
