Area of Triangle - Coordinate Geometry
The area of the triangle is option A) according to the options given in the diagram [tex]1/2 * \sqrt{(x1^2 + y1^2) * ( x2^2 + y2^2 )}[/tex]
Step-by-step 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
=> [tex]\sqrt{ x1^2 + y1^2}[/tex]
The length of BC is: (x₂-0)^2 + (y₂-0)^2
=> [tex]\sqrt{ x2^2 + y2^2}[/tex]
Hence the area is
Area = (1/2) * [tex]\sqrt{(x1^2 + y1^2)}[/tex] * [tex]\sqrt{x2^2 + y2^2 )} \\[/tex]
Area = [tex]1/2 * \sqrt{(x1^2 + y1^2) * ( x2^2 + y2^2 )}[/tex]
Hence, the area of the triangle is option A) according to the options given in the diagram
