Draw the graph of the pair of equations 2x + y = 4 and 2x - y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle
Solution:
Table for line 2x + y = 4
y = 4 - 2x.
|
x |
0 |
2 |
|---|---|---|
|
y |
4 |
0 |
Table for line 2x - y = 4
y = 2x - 4.
|
x |
0 |
2 |
|---|---|---|
|
y |
-4 |
0 |
Graphical representation of both lines are as follows :
In this, both lines and y-axis form ∆ABC.
Hence, the vertices of a ∆ABC are A(0, 4), B(2, 0) and C(0, - 4)
The area of ∆ABC = 2 × Area of ∆AOB
The area of ∆ABC = 2 × 1/2 × 4 × 2 = 8sq units.
Therefore, the area of the triangle is 8 sq units.
✦ Try This: Draw the graph of the pair of equations 2x + y = 6 and 2x - y = 6. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 12
Draw the graph of the pair of equations 2x + y = 4 and 2x - y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle
Summary:
Drawing the graph of the pair of equations 2x + y = 4 and 2x - y = 4 the vertices of the triangle formed by these lines and the y - axis is A(0, 4), B(2, 0) and C(0, - 4) and the area of the triangle is 8 sq units.
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