Prove that the area of the triangle whose vertices are `(t ,t-2),(t+2,t+2)a n d(t+3,t)` is independent of `tdot`

Explanation

To prove that the area of the triangle with vertices \((t, t-2)\), \((t+2, t+2)\), and \((t+3, t)\) is independent of \(t\), we can use the formula for the area of a triangle given by the coordinates of its vertices. The area \(A\) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) can be calculated using the determinant:

\[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

### Step-by-Step Solution:

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