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Question

Draw the graphs of the pair of linear equations x y + 2 = 0 and 4x y 4 = 0 . Calculate the area of the triangle formed by the lines so drawn and the x-axis .

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Solution

The given linear equations are


x − y

+ 2 = 0 .....(i)


4

x − y

− 4 = 0 .....(ii)


For (i), we have

x0−2
y20


For (ii), we have

x01
y−40


The graph of the lines represented by the given equations is shown below:



The triangle thus obtained has the vertices A(2, 4), B(−2, 0) and D(1, 0).


∴ Area of triangle ADB


=(1/2)×3×4=6 square units


Thus, the area of the triangle formed by the given lines and the

x

-axis is 6 square units.


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