Answer:
A. [tex]A = \frac{1}{2}\cdot \sqrt{(x_{2}^{2}+y_{2}^{2})\cdot (x_{2}^{2}+y_{2}^{2})}[/tex]
Step-by-step explanation:
From Geometry, we know that the area of the triangle ([tex]A[/tex]) is equal to:
[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (1)
Where:
[tex]b[/tex] - Base.
[tex]h[/tex] - Height.
By Pythagorean Theorem, we derive expressions for the base and the height of triangle. That is:
[tex]h = \sqrt{(-x_{1}-0)^{2}+(y_{1}-0)^{2}}[/tex]
[tex]h = \sqrt{x_{1}^{2}+y_{1}^{2}}[/tex] (2)
[tex]b = \sqrt{(x_{2}-0)^{2}+(y_{2}-0)^{2}}[/tex]
[tex]b = \sqrt{x_{2}^{2}+y_{2}^{2}}[/tex] (3)
By (2) and (3), we expand (1):
[tex]A = \frac{1}{2}\cdot \sqrt{(x_{2}^{2}+y_{2}^{2})\cdot (x_{2}^{2}+y_{2}^{2})}[/tex]
Hence, correct answer is A.
