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 xx "base" xx "height"`

= `1/2 xx 6 xx 2` sq unit

=  6 sq units