Answer:
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!