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:

Answer: Option B

Solution

Answer: Option B

Solution:

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

$$\begin{array}{rl}& \text{Area of }\Delta OCD=\frac{1}{2}\times 4\times 4=8\text{ sq}\text{. units}\\ & \therefore \text{Area of }\Delta OCD=\frac{1}{3}\text{Area of }\Delta OAB\end{array}$$