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
Solution:
Given, the linear equations are
x - y + 2 = 0
4x - y - 4 = 0
We have to draw the graph of the pair of linear equations and calculate the area of the triangle formed by the lines drawn and the x-axis.
The equation x - y + 2 = 0 can be written as y = x + 2
When x = 0, y = 0 + 2 = 2
When x = -2, y = -2 + 2 = 0
The equation 4x - y - 4 = 0 can be written as y = 4x - 4
When x = 0, y = 0 - 4 = -4
When x = 1, y = 4(1) - 4 = 0
Plotting the graph using the points (0, 2) (-2, 0) (0, -4) and (1, 0)
The vertices of the triangle is A(-2, 0) B(1, 0) and C(2, 4)
By using the distance formula,
\(distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)
\(AB=\sqrt{(1-(-2))^{2}+(0-0)^{2}}\\=\sqrt{(1+2)^{2}}\\=\sqrt{3^{2}}\\=3\)
Area of the triangle = (1/2)(base)(height)
Base = 3 units
Height = 4 units
Area = (1/2)(3)(4)
= 12/2
= 6 square units.
Therefore, the area of the triangle is 6 square units.
ā¦ Try This: Draw the graphs of the pair of linear equations x + y - 2 = 0 and x - y - 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis
ā Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Sample Problem 3
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
Summary:
The graphs of the pair of linear equations x - y + 2 = 0 and 4x - y - 4 = 0 is shown above. The area of the triangle formed by the lines so drawn and the x-axis is 6 square units.
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