Question:
Draw the graphs of the following equations:
$2 x-3 y+6=0$
$2 x+3 y-18=0$
$y-2=0$
Find the vertices of the triangle so obtained. Also, find the area of the triangle.
Solution:
The given equations are
$2 x-3 y+6=0$..(i)
$2 x+3 y-18=0$..(ii)
$y-2=0$..(iii)
The two points satisfying (i) can be listed in a table as,
The two points satisfying (ii) can be listed in a table as,
It is seen that the coordinates of the vertices of the obtained triangle are
$A(3,4), B(0,2), C(6,2)$
Area of $\triangle A B C=\frac{1}{2} \times$ Base $\times$ height $=\frac{1}{2} \times 6 \times 2 \mathrm{sq}$ units $=6 \mathrm{sq}$ units