What is the length of vw? a) 16 units b) \sqrt{x} 13 c)20 units d) \sqrt{x} 20

The answer is:  " 4.47 units " .

Explanation:

Note the Pythagorean theorem for right triangles:

→ a² + b² = c² ; 

Solve for the "positive value of "c" ; 

in which "c" is the "hypotenuse" ; which is the length of VW ; 

in which one side of a right triangle is from:
 
"Point W" {coordinate of "(-4, -2)" to "(-2, -2)" ; which is "2 units" long; 

and another side of the right triangle is from:

  "(-2, -2)" to "(2, 2)" ; which is:  "4 units long)

c² = 2² + 4² ; 

Solve for the "positive value" of "c" ;  which is the "hypotenuse" ; which is the length of VW .


c² = 4 + 16 = 20 ; 

c² = 20 ; 

Take the "positive square root" of each side of the equation; to solve for "c" ; 

 ⁺√(c²) = ⁺√20; 

to get: 

→  c = √4√5 = " 2√5 units " ; 

or; using calculator:  " √20 = 4.4721359549995794 " ;  

→ round to:  "4.47 units" .