Question

What is the area of the triangle in the diagram?
OA / (+? + , ?) (= ² + 4₂²)
B. IV (5,2 – 177)(y22 – y?)
© C. (,2 + y 2)(032 + y;?)
OD. 2/(*;? – 5,2)(,2 – y?)

Answer 1

the answer is c (2,+y2)(032+y;?)

Answer 2

Area of Triangle - Coordinate Geometry

 The area of the triangle is option A) according to the options given in the diagram $1/2 * \sqrt{(x1^2 + y1^2) * ( x2^2 + y2^2 )}$

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

=>  $\sqrt{ x1^2 + y1^2}$

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

 =>  $\sqrt{ x2^2 + y2^2}$

Hence the area is

Area = (1/2) * $\sqrt{(x1^2 + y1^2)}$ * $\sqrt{x2^2 + y2^2 )}$

Area = $1/2 * \sqrt{(x1^2 + y1^2) * ( x2^2 + y2^2 )}$

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