Respuesta :

Answer:

A

Step-by-step explanation:

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

[tex]A=\frac{1}{2}bh[/tex]

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:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

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:

[tex]d=\sqrt{{(0-x_1)^2+(0-y_1)^2[/tex]

Simplify:

[tex]d=\sqrt{(-x)^2+(-y)^2[/tex]

We can remove the negative:

[tex]d=\sqrt{((-1)x_1)^2+((-1)y_1)^2[/tex]

[tex]d=\sqrt{x_1\!^2+y_1\!^2}[/tex]

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:

[tex]d=\sqrt{(x_2-0)^2+(y_2-0)^2[/tex]

Simplify. So, our height is:

[tex]d=\sqrt{(x_2)^2+(y_2)^2[/tex]

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

[tex]A=\frac{1}{2}(\sqrt{(x_1)^2+(y_1)^2)}(\sqrt{(x_2)^2+(y_2)^2})[/tex]

We can combine the square roots by multiplying. So:

[tex]A=\frac{1}{2}\sqrt{(x_1\!^2+y_1\!^2)(x_2 \!^2+y_2\!^2)[/tex]

The answer choice that represents this is A.

So, our answer is A.

And we're done!

Answer:

a

Step-by-step explanation:

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