Answer:
[tex] \sqrt{13} [/tex]
Option D is the correct option.
Step-by-step explanation:
Given,
A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )
Let,
A ( 4 , 5 ) → ( x1 , y1 )
B ( 2 , 2 ) → ( x2 , y2 )
Now, finding the length of AB
Use the distance formula to find the length of AB
[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
plug the values
[tex] = \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} } [/tex]
Calculate the difference
[tex] = \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} } [/tex]
Evaluate the power
[tex] = \sqrt{4 + 9} [/tex]
Add the numbers
[tex] = \sqrt{13} [/tex]
Hope this helps..
Best regards!!