# determine graphically the coordinates of the vertices of the triangle bounded by 2x-3y+6=0;2x+3y-18+0;y-2=0,also find the area of this triangle

On plotting given lines, we get the figure as shown below:

Here, Red line represents 2x – 3y + 6 = 0; Blue line represents 2x + 3y – 18 = 0; and Green line represents y – 2 = 0

Now, Area of Triangle = 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))

Here, (x1,y1) = (3,4); (x2,y2) = (0,2) and (x3,y3) = (6,2)

So, area of triangle = 1/2[3(2 – 2) + 0(2 – 4) + 6(4 – 2)]

=1/2 [ 3(0) + 0(-2) + 6(2)]

=1/2[0 + 0 + 12]

=1/2 [12]

=6