Question

WILL GIVE BRIANLIEST!! plato

Answer 1

A.
`A = (1)/(2)\cdot \sqrt{(x_(2)^(2)+y_(2)^(2))\cdot (x_(2)^(2)+y_(2)^(2))}`

Explanation:

From Geometry, we know that the area of the triangle (
`A`) is equal to:

`A = (1)/(2)\cdot b\cdot h` (1)

Where:

`b` - Base.

`h` - Height.

By Pythagorean Theorem, we derive expressions for the base and the height of triangle. That is:

`h = \sqrt{(-x_(1)-0)^(2)+(y_(1)-0)^(2)}`

`h = \sqrt{x_(1)^(2)+y_(1)^(2)}` (2)

`b = \sqrt{(x_(2)-0)^(2)+(y_(2)-0)^(2)}`

`b = \sqrt{x_(2)^(2)+y_(2)^(2)}` (3)

By (2) and (3), we expand (1):

`A = (1)/(2)\cdot \sqrt{(x_(2)^(2)+y_(2)^(2))\cdot (x_(2)^(2)+y_(2)^(2))}`

Hence, correct answer is A.