Question

Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Answer 1

Table for line 2x + y = 4

⇒ y = 4 – 2x

x	0	2
y	4	0

And table for line 2x – y = 4

⇒ y = 2x – 4

x	0	2
y	– 4	0

Graphical representation of both lines are as follows:

Here, both lines and y-axis form ∆ABC.

Hence, the vertices of a ∆ABC are A(0, 4), B(2, 0) and C(0, – 4)

∴ Required area of ∆ABC = 2 × Area of ∆AOB 

= `2 xx 1/2 xx 4 xx 2`

= 8 sq.units

Hence, the required area of the triangle is 8 sq.units.