Identify the translation rule on a coordinate plane that verifies that triangle a(-5,1), b(-2,7), c(0,1) and triangle a'(-6,0), b'(-3,6), c'(-1,0) are congruent. a) (x, y) → (x - 1, y - 1) b) (x, y) → (x + 2 , y + 1) c) (x, y) → (x - 2, y + 1) d) the triangles are not congruent

We can compare coordinates of points and their images ,and
we need to find the rule
(x, y) > (x', y')
A(-5,1)>A'(-6,0)
-5+a=-6,     a=-1,  x--->x' , x-1=x'
1+b=0, b=-1,     y>y', y-1=y'
B(-2,7) > A'(-3,6)
-2+a= -3,    a=-1 ,   x--->x' , x-1=x'
7+b=6,   b=-1,       y>y', y-1=y'
C(0,1) >C'(-1,0)
0+a= -1,    a=-1 x--->x' , x-1=x'
 1+b=0, b=-1 ,  y>y', y-1=y'
Now we can see that  (x, y)> (x-1,y-1)  Answer A