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Kisachek [45]
3 years ago
8

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

Chemistry
1 answer:
AlexFokin [52]3 years ago
7 0

Answer:

Area = \frac{1}{2}|x_1(y_2 - y_3)+x_2(y_3 - y_1)+x_3(y_1 - y_2)|

Area = 2\ units^2

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 = \frac{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 = \frac{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 = \frac{1}{2}|0(1-3) + 2(3-3) + 2(3-1)|

Area = \frac{1}{2}| 2*0 + 2*2|

Area = \frac{1}{2}| 0 + 4|

Area = \frac{1}{2}|4|

Area = \frac{1}{2} * 4

Area = 2\ units^2

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