Math, asked by pg7758740, 16 days ago

31. Find the area of a triangle ABC whose vertices are A(2, 2) B(3,4) and C (–1,3).​

Answers

Answered by TeacherX
26

Step-by-step explanation:

Area of triangle with vertices A (2,2) B(3,4) C(-1,3)

= 1/2[ 2(4-3) + 3(3-2) + (-1)( 2-4) ]

= 1/2 [ 2(1) + 3(1) - 1(-2) ]

= 1/2 [ 2+3+2]

= 7/2

Answered by VineetaGara
11

Given,

For a ∆ABC,

Coordinates of point A = (2,2)

Coordinates of point B = (3,4)

Coordinates of point C = (-1,3)

To find,

The area of the ∆ABC.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically, according to the coordinate geometry formula;

The area of a triangle whose x and y coordinates of the three vertices are known is calculated as follows:

Area = 1/2{Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)}

{Statement-1}

Now, according to the question;

For the given ∆ABC,

Ax = 2

Ay = 2

Bx = 3

By = 4

Cx = -1

Cy = 3

Now, according to the statement-1;

The area of the ∆ABC

= 1/2{Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)}

= 1/2{(2)(4 - 3) + (3)(3 - 2) + (-1)(2 - 4)}

= 1/2{(2)(1) + (3)(1) + (-1)(-2)}

= 1/2 × (2+3+2) = 7/2 square units

= 3.5 square units

Hence, the area of the ∆ABC is equal to 3.5 square units.

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