Question

100 points! explain well for brainliest

Answer 1

Answer:

a

Step-by-step explanation:

Answer 2

Answer:

A

Step-by-step explanation:

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

$A=\frac{1}{2}bh$

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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

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:

$d=\sqrt{{(0-x_1)^2+(0-y_1)^2$

Simplify:

$d=\sqrt{(-x)^2+(-y)^2$

We can remove the negative:

$d=\sqrt{((-1)x_1)^2+((-1)y_1)^2$

$d=\sqrt{x_1\!^2+y_1\!^2}$

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:

$d=\sqrt{(x_2-0)^2+(y_2-0)^2$

Simplify. So, our height is:

$d=\sqrt{(x_2)^2+(y_2)^2$

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

$A=\frac{1}{2}(\sqrt{(x_1)^2+(y_1)^2)}(\sqrt{(x_2)^2+(y_2)^2})$

We can combine the square roots by multiplying. So:

$A=\frac{1}{2}\sqrt{(x_1\!^2+y_1\!^2)(x_2 \!^2+y_2\!^2)$

The answer choice that represents this is A.

So, our answer is A.

And we're done!