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RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2 Solutions

Question - 41 : - 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. [NCERT Exemplar]

Answer - 41 : -

For drawing the graphs of the given equations, we find two solutions of each of the equations, which are given in table.
Plot the points A (0,2), B (-2,0), P (0, -4) and Q (1,0) on the graph paper, and join the points to form the lines AB and PQ as shown in the figure.
 
We observe that there is a point R (2,4) common to both the lines AB and PQ. The triangle formed by these lines and the x-axis is BQR.
The vertices of this triangle are B (-2, 0), Q (1, 0) and R (2, 4).
We know that;
Area of triangle = x Base x Altitude
Here, Base = BQ = BO + OQ = 2 + 1 = 3 units
Altitude = RM = Ordinate of R = 4 units.
So, area of ABQR = x 3 x 4 = 6 sq. units

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