A translation maps A ti A' and B to B'. We know AA'=6, AB=5, and AB'=5 find BA'

Since a translation preserves distances, we can leverage the given information to solve for BA'. Here's how:

 

Consider the Triangle AAB':

 

We know AB = 5 and AA' = 6. These two segments form the legs of a right triangle (triangle AAB') with the hypotenuse (AB') unknown.

 

Pythagorean Theorem:

 

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (c²) is equal to the sum of the squares of the legs (a² and b²). In this case:

 

(AB')² = (AA')² + (AB)²

 

Substitute Known Values:

 

(AB')² = (6)² + (5)²

 

Solve for AB':

 

(AB')² = 36 + 25 = 61

 

Take the square root of both sides:

AB' = sqrt(61)