No 20 points
using the transformation t: (x, y) (x + 2, y + 1). find the distance named.

find the distance ca (the answer must be in the square root form)

 The length of AC  is:  " 2√2 units " . 

Explanation:

Note:   (not to scale):

     
     C
      |    \
      |      \ 
2   |         \   "c"   
     |--         \
     |              \ 
     |_|\ A
    •        2
(point    
–at which
right angle forms)

Use the "Pythagorean theorem"  (since this is a right triangle) to solve for the length of AC — which  is represented by "c" :

  a²  +  b²  =  c² ;

↔  c²  =  a² + b² ;  Solve for "c" ;

Given:  "a = 2 ;  b = 2 " ;

→   c²  =  2² + 2²

→   c²  =  4 + 4 ;

→   c²  = 8 ; 

Take the "positive square root" of each side of the equation;
     to isolate "c" on one side of the equation; & to solve for "c" ; 

→  √(c²) = √8 ; 

→ c = √8 ; 

→  √8 = √4 * √2 = 2√2 .

 The length of AC  is:  " 2√2 units " .