100 points! explain well for brainliest

A

Step-by-step explanation:

Remember that the formula for the area of a triangle is:

In this case, our base will be the distance from the origin point (0, 0) to (x₁, y₁).

Our height will be the distance from the origin point (0, 0) to (x₂, y₂).

So, let's find each of the distances using the distance formula:

BASE:

Let's let (x₁, y₁) be itself and let's let (0, 0) be (x₂, y₂). Substitute this into the distance formula. This yields:

Simplify:

We can remove the negative:

And this is the length of our base.

HEIGHT:

Let' let (0, 0) be (x₁, y₁) and (x₂, y₂) be itself. Substitute them into our distance formula:

Simplify. So, our height is:

Therefore, substitute the base and the height for b and h in our equation yields:

We can combine the square roots by multiplying. So:

The answer choice that represents this is A.

So, our answer is A.

And we're done!

20%

step-by-step explanation: