Question

Write down the formula to find the area of a triangle whose vertices are \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\).

Hint:

For area of a triangle using coordinates, always use modulus signs because area cannot be negative.

Answer 1

Step 1: Recall the coordinate geometry formula.}
The area of a triangle whose vertices are given in coordinate form can be found using the determinant formula.

Step 2: Write the standard formula.}
If the vertices of the triangle are \((x_1,y_1)\), \((x_2,y_2)\), and \((x_3,y_3)\), then its area is:
\[ \text{Area} = \frac{1}{2}\left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
Step 3: Mention the absolute value.}
Absolute value is taken because area is always positive, even if the expression inside the bracket becomes negative.

Step 4: State the final formula.}
Hence, the required formula is:
\[ \boxed{\text{Area} = \frac{1}{2}\left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right|} \]