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
Solution:
From the above question, we have the equation as,
2x - y - 4 = 0,
x = 3 , x = 5.
|
x |
0 |
2 |
|---|---|---|
|
y |
-4 |
0 |
Plotting the points (0, -4) and (2, 0) and joining these points, we get the graph of 2x - y - 4 = 0.
Draw the lines x = 3 and x = 5.
From the graph, ABCD is the quadrilateral formed by given lines and x - axis.
Area of quadrilateral ABCD = 1/2 x (distance between parallel lines) x (sum of parallel sides).
Area of quadrilateral ABCD = 1/2 x AB x (AD + BC)
Area of quadrilateral ABCD = 1/2 x 2 x (2 + 6). [∵ AB = OB - OA = 5-3 = 2, AD = 2 and BC = 6]
Area of quadrilateral ABCD = 8 sq. units.
Therefore, the area of the quadrilateral formed by the lines and the x-axis is 8 sq. units.
✦ Try This: Draw the graphs of the equations x = 2, x = 4 and 2x - y - 4 = 0. Also find the area of the quadrilateral formed by the lines and the x-axis
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 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
Summary:
The graphs of the equations x = 3, x = 5 and 2x - y - 4 = 0 is mentioned above. The area of the quadrilateral formed by the lines and the x-axis is 8 sq. units
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