Question

What is the area of triangle ABC with vertices A(x¹,y¹), B(x²,y²)and C (x³,y³)??????????
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Answer 1

`Area = (1)/(2)|x_1(y_2 - y_3)+x_2(y_3 - y_1)+x_3(y_1 - y_2)|`

`Area = 2\ units^2`

Step-by-step explanation:

Given

`A = (x_1,y_1)`

`B = (x_2,y_2)`

`C = (x_3,y_3)`

Required

Determine the area

The area of a triangle is :

`Area = (1)/(2)|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|`

By substituting values for the x and y coordinates of A, B and C;

We have:

`Area = (1)/(2)|x_1(y_2 - y_3)+x_2(y_3 - y_1)+x_3(y_1 - y_2)|`

So:

For instance

`A = (0,3)`

`B= (2,1)`

`C = (2,3)`

The area is:

`Area = (1)/(2)|0(1-3) + 2(3-3) + 2(3-1)|`

`Area = (1)/(2)| 2*0 + 2*2|`

`Area = (1)/(2)| 0 + 4|`

`Area = (1)/(2)|4|`

`Area = (1)/(2) * 4`

`Area = 2\ units^2`