The area of triangle ABC is 20 cm². The coordinates of vertex A are (–5, 0) and those of B are (3, 0). The vertex C lies on the line x – y = 2. The coordinates of C are

Let any point on the line x – y = 2 be C(h, h – 2).

The given area of $∆ABC$ is $\left|\left|\frac{1}{2}\right|\begin{array}{ccc}h& h-2& 1\\ -5& 0& 1\\ 3& 0& 1\end{array}\right|=20\text{ (or) }\left|8\right(h-2\left)\right|=40$

(or) $\mathrm{h}-2=\pm 5\text{ (or) }\mathrm{h}=7,-3$

Hence, the points are (7, 5) and (–3, –5)