Question

Draw the graphs of the following equations:

2x − 3y + 6 = 0
2x + 3y − 18 = 0
y − 2 = 0

Find the vertices of the triangle so obtained. Also, find the area of the triangle.

Answer 1

The given equations are

2x − 3y + 6 = 0 ......(i)

2x + 3y − 18 = 0 ........(ii)

y − 2 = 0 ...........(iii)

The two points satisfying (i) can be listed in a table as

x	-3	6
y	0	6

The two points satisfying (ii) can be listed in a table as,

x	0	9
y	6	0

The two points satisfying (iii) can be listed in a table as,

x	-1	8
y	2	2

Now, graph of equations (i), (ii) and (iii) can be drawn 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 ΔABC = 1/2 x Base x height =  1/2 x 6 x 2 sq unit =  6 sq units