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

For equation, 2x - 3y + 6 = 0

Coordinates satisfying graph are,

x	0	-3
y	2	0

For equation, 2x + 3y - 18 = 0

Coordinates satisfying graph are,

x	0	9
y	6	0

and y - 2 = 0

⇒ y = 2, which is a straight line parallel to x - axis intersecting the y - axis at 2

On plotting all the three line on graphs, we get the graph as follows

On observing from graph,

Vertices of the triangle obtained are

(0, 2), (3, 4) and (6, 2)

Height of triangle = 4 – 2 = 2

Base of the triangle = 6

Area of the triangle

= \(\frac{1}{2}\)x Base x Height

= \(\frac{1}{2}\)x 6 x 2

= 6 square units