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.

Triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'. The rule of translation is

Step-by-step explanation:

Given information: In triangle ABC, A(-5,1), B(-2,7), C(0,1). In triangle A'B'C', A'(-6,0), B'(-3,6), C'(-1,0).

Let the rule of translation be

where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b<0, then the graph shifts b units up and if b>0, then the graph shifts b units down.

It is given that A(-5,1) and A'(-6,0).

On comparing both sides, we get

The value of a is 1 and value of b is 1. So, the rule of translation is

Therefore the triangle ABC translate 1 unit left and 1 units down to get the triangle A'B'C'.