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 * √((x1^2 + y1^2) * ( x2^2 + y2^2 ))`

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

=>
`√( x1^2 + y1^2)`

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

=>
`√( x2^2 + y2^2)`

Hence the area is

Area = (1/2) *
`√((x1^2 + y1^2))` *
`√(x2^2 + y2^2 )) \\`

Area =
`1/2 * √((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