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 \(A(-5,1)\) --------> \(A'(-3,2)\)
Find the rule in the x-coordinate
\(-5+x=-3\\ x=-3+5\\ x=2\)
x--------> x+2
Find the rule in the y-coordinate
\(1+y=2\\ y=2-1\\ y=1\)
y--------> y+1
The translation rule is
\((x,y)------> (x+2,y+1)\)
Verify vertex B
\(B(-2,7)\)-------> \((x+2,y+1)\) ------> \((-2+2,7+1)\)--------> \(B'(0,8)\) ------> is ok
Verify vertex C
\(C(0,1)\)-------> \((x+2,y+1)\) ------> \((0+2,1+1)\)--------> \(C'(2,2)\) ------> is ok
The three vertices have the same rule, therefore the triangles are congruent
the answer is
The translation rule is
\((x,y)------> (x+2,y+1)\)
