Geometry

Step 1: Formula for the Area of a Triangle.
The formula for the area of a triangle given its vertices

A(x_1%2C%20y_1)

B(x_2%2C%20y_2)

, and

C(x_3%2C%20y_3)

is:

%5Ctext%7BArea%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%7C%20x_1(y_2%20-%20y_3)%20%2B%20x_2(y_3%20-%20y_1)%20%2B%20x_3(y_1%20-%20y_2)%20%5Cright%7C

Step 2: Apply the given coordinates.
For

A(2%2C%203)

B(-1%2C%200)

, and

C(2%2C%20-4)

, we substitute the coordinates into the formula:

%5Ctext%7BArea%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%7C%202(0%20-%20(-4))%20%2B%20(-1)((-4)%20-%203)%20%2B%202(3%20-%200)%20%5Cright%7C

%5Ctext%7BArea%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%7C%202(D)%20%2B%20(-1)(-7)%20%2B%202(C)%20%5Cright%7C

%5Ctext%7BArea%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%7C%208%20%2B%207%20%2B%206%20%5Cright%7C%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2021%20%3D%2010.5

Step 3: Conclusion.
Therefore, the area of the triangle is

10.5

square units.

Final Answer: 10.5.

Chapter Questions
1 MCQs