The correct option is A: AB = BA is an example of the reflexive property.
We can define AB as the distance between points A and B.
Makes sense to think that AB = BA, here we are saying:
The distance between points A and B is equal to the distance between points B and A.
Now, notice that the symmetric property of the equality says that:
a = x, then x = a.
While the reflexive property says that:
x = x.
Now, we know that the distance between two points A(x₁, y₁) and B(x₂, y₂) (this can be generalized for any dimension, but let's use 2D for simplicity) can be written as:
[tex]AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Now, we can notice that:
[tex](x_1 - x_2)^2 = (x_2 - x_1)^2[/tex]
Replacing these in the above equation we get:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = BA[/tex]
then BA = AB.
So BA and AB are the same thing, then this is an x = x kind of thing, so we can conclude that AB = BA is an example of the reflexive property.
If you want to read more, you can read:
https://brainly.com/question/862440
