Formula of Area of triangle in coordinate geometry

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To find the area of a triangle in coordinate geometry, you can use the formula known as the "Heron's formula." It is based on the lengths of the sides of the triangle. Here's how you can find it:

1. First, identify the coordinates of the three vertices of the triangle. Let's call them A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃).

2. Calculate the lengths of the three sides of the triangle using the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)

So, the lengths of the three sides can be calculated as:
AB = √((x₂ - x₁)² + (y₂ - y₁)²)
BC = √((x₃ - x₂)² + (y₃ - y₂)²)
AC = √((x₃ - x₁)² + (y₃ - y₁)²)

3. Next, calculate the semi-perimeter of the triangle, denoted as s. It is defined as:
s = (AB + BC + AC) / 2

4. Finally, apply Heron's formula to find the area (A) using the lengths of the sides and the semi-perimeter:
A = √(s(s - AB)(s - BC)(s - AC))

Now you have the formula to find the area of a triangle in coordinate geometry using the coordinates of its vertices.