Question

Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x–axis.

Answer 1

Given equation of lines x = 3, x = 5 and 2x – y – 4 = 0

Table for line 2x – y – 4 = 0

x	0	2
y	–4	0

Plotting the graph, we get,

∴ Area of quadrilateral ABCD = `1/2` × distance between parallel lines (AB) × (AD + BC)  ...[Since, quadrilateral ABCD is a trapezium]

= `1/2 xx 2 xx (6 + 2)`  ...[∵ AB = OB – OA = 5 – 3 = 2, AD = 2 and BC = 6]

= 8 sq.units