The statement ab = ab is an example of the property

a. reflexive
b. symmetric
c. proof
d. transitive

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:

Now, we can notice that:

Replacing these in the above equation we get:

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.

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the correct answer is d

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