The graph of 3x + 4y - 24 = 0 forms a triangle OAB with the co-ordinate axes, where O is the origin. Also the graph of x + y + 4 = 0 forms a triangle OCD with the coordinate axes. Then the area of ΔOCD is equal to:

Solution (By Examveda Team)

$$\eqalign{ & 3x + 4y - 24 = 0 \cr & \Rightarrow 3x + 4y = 24 \cr & \Rightarrow \frac{{3x}}{{24}} + \frac{{4y}}{{24}} = 1 \cr & \Rightarrow \frac{x}{8} + \frac{y}{6} = 1 \cr & {\text{Area of }}\Delta OAB = \frac{1}{2} \times 6 \times 8 = 24{\text{ sq}}{\text{. units}} \cr & {\text{And,}} \cr & x + y + 4 = 0 \cr & \Rightarrow x + y = - 4 \cr & \Rightarrow \frac{x}{{\left( { - 4} \right)}} + \frac{y}{{\left( { - 4} \right)}} = 1 \cr} $$

$$\eqalign{ & {\text{Area of }}\Delta OCD = \frac{1}{2} \times 4 \times 4 = 8{\text{ sq}}{\text{. units}} \cr & \therefore {\text{Area of }}\Delta OCD = \frac{1}{3}{\text{Area of }}\Delta OAB \cr} $$