Let A ≡ (x, y), B ≡ (2, 1), C ≡ (3, –2) Area of ΔABC = \(rac{1}{2}\) |{x1 (y2 – y3) + x2(y3 – y1) + x3(y1 – y2)}|= \(rac{1}{2}\) | \(x\)(1 + 2) + 2(–2 – y) + 3(y – 1) | = \(rac{1}{2}\) | 3\(x\) – 4 – 2y + 3y – 3 | = \(rac{1}{2}\) | 3\(x\) + y – 7 |Given \(rac{1}{2}\) | 3\(x\) + y – 7 | = 5⇒ | 3\(x\) + y – 7 | = 10 ⇒ 3\(x\) + y – 7 = 10 or –(3\(x\) + y – 7) = 10 ⇒ 3\(x\) + y = 17 or 3\(x\) + y = –3Case I. 3\(x\) + y = 17. Also given y = \(x\) + 3 ∴ 3x + \(x\) + 3 = 17 ⇒ 4\(x\) = 14 ⇒ \(x\) = \(rac{7}{2}\) ⇒ y = \(rac{7}{2}\) + 3 = \(rac{13}{2}\)Case II. 3\(x\) + y = –3, y = \(x\) + 3∴ 3\(x\) + \(x\) + 3 = –3 ⇒ 4\(x\) = – 6 ⇒ \(x\) = \(rac{-3}{2}\) ⇒ y = \(rac{-3}{2}\) + 3 = \(rac{3}{2}\)∴ Co-ordinates of A are \(\bigg(rac{7}{2},rac{13}{2}\bigg)\) or \(\bigg(rac{-3}{2},rac{3}{2}\bigg)\)