Question

Draw the graph of two lines, whose equations are 3x − 2y + 6 = 0 and x + 2y − 6 = 0 on the same graph paper. Find the area of triangle formed by the two lines and x-axis.

Answer 1

The points satisfying the equation 3x − 2y + 6 = 0 are:

And, the points satisfying the equation x + 2y − 6 = 0 are:

The graph of the given two lines is as follows:

The vertices of the triangle formed by the given lines and x-axis are B(6, 0), A(−2, 0) and C(0, 3).

Now,

$$\begin{gathered} \mathrm{ar}\left(∆\mathrm{ABC}\right)=\frac{1}{2}\times \mathrm{AB}\times \mathrm{OC} \\ =\frac{1}{2}\times 8\times 3 \\ =12\mathrm{square}\mathrm{units} \end{gathered}$$

So, the area of the triangle so formed is 12 square units.