Question

Question 3
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

$\begin{array}{ccc}X& 0& 2\\ Y=2x-4& -4& 0\\ Points& P& Q\end{array}$
Draw the points P (0, - 4) and Q (2, 0) and joint these points and form a line PQ also draw the lines x = 3 and x = 5

$\therefore$ Area of quadrilateral ABCD $=\frac{1}{2}\times$ distance between parallel lines $\left(AB\right)\times (AD+BC)$
[since, Quadrilateral ABCD is a trapezium]
$=\frac{1}{2}\times 2\times (6+2)[\therefore AB=OB-OA=5-3=2,AD=2andBC=6]$
= 8 sq units
Hence, the required area of the quadrilateral formed by the lines and the X – axis is 8 sq units