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

B would be it i think

Answer 2

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)`