Area of Triangle - Coordinate Geometry
The area of the triangle is option A) according to the options given in the diagram

Explanation:
The given triangle is a right triangle with co-ordinates A(x1,y1),B(x2,y2),C(0,0)
And thus its area is given by the formula A= ( ½) *( b* h) where b is base of triangle and h is height of the triangle
Let Base = AC and Height = BC
The length of AC is : (x₁-0)² + (y₁-0)²
=>

The length of BC is: (x₂-0)^2 + (y₂-0)^2
=>

Hence the area is
Area = (1/2) *
*

Area =

Hence, the area of the triangle is option A) according to the options given in the diagram