The area of a triangle is 5. Two of its vertices are A(2, 1) and B(3, –2). The third vertex C is on y = x + 3. Find C

As C lies on the line y =x + 3, let the coordinates of C be $(\mathrm{\lambda },\mathrm{\lambda }+3).\text{ Also, }\mathrm{A}\equiv (2,1),\mathrm{B}\equiv (3,-2)$. Then the area of $\mathrm{△}\mathrm{ABC}$ is given by $4\mathrm{\lambda }=14\text{ or }4\mathrm{\lambda }=-6$ i.e., $\mathrm{\lambda }=\frac{7}{2}\text{ or }\mathrm{\lambda }=-\frac{3}{2}$