Question

Look at triangle ABC

A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)
1
5 -4 -3 -2 -1 0
1
23
4
5
-1
N
-3
-4
5
What is the length of side AB of the triangle?

A) 3
B) 5
C) square root of 6
D) square root of 13

Answer 1

`√(13)`

Option D is the correct option.

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

`= \sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) }`

plug the values

`= \sqrt{ {(2 - 4)}^(2) + {(2 - 5)}^(2) }`

Calculate the difference

`= \sqrt{ {( - 2)}^(2) + {( - 3)}^(2) }`

Evaluate the power

`= √(4 + 9)`

Add the numbers

`= √(13)`

Hope this helps..

Best regards!!