Question

Identify the translation rule on a coordinate plane that verifies that triangle A(-5,1), B(-2,7), C(0,1) and triangle A'(-3,2), B'(0,8), C'(2,2) are congruent

Answer 1

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

$(x,y)------> (x+2,y+1)$

Answer 2

B would be it i think