Question

The line 4x + 3y – 12 = 0 cuts the coordinate axes at A and B. The area of ΔOAB is _________.

Answer 1

The given equation is 4x + 3y – 12 = 0 ...(i)

Solving equation (i), we get

$$\begin{gathered} 4x+3y-12=0 \\ \Rightarrow 3y=12-4x \\ \Rightarrow y=\frac{12-4x}{3} \end{gathered}$$

When x = 0, y = 4
When x = 3, y = 0

x	0	3
y	4	0

On plotting these points on a graph, we get



We can see that OA = 3 units and OB = 4 units

Area of ΔOAB = $\frac{1}{2}\times OA\times OB$
= $\frac{1}{2}\times 3\times 4$
= 6

Hence, the area of ΔOAB is 6 square units.