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

Answer:

$\sqrt{13}$

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

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

plug the values

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

Calculate the difference

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

Evaluate the power

$= \sqrt{4 + 9}$

Add the numbers

$= \sqrt{13}$

Hope this helps..

Best regards!!