Write any four linear equations in two variables and plot them on a graph paper. Name the shape enclosed by them and find its area.
Answers
Linear equations
To find: the name and area of the shape bounded by any four linear equations
Solution:
We consider four linear equations:
x + 3y = 1
3x - y = 1
3x - y = 10
x + 3y = 10
Drawing the above linear equations in two variables on graph paper, we find a square bounded by them.
Here x + 3y = 1 and x + 3y = 10 are parallel sides of the square; so are the sides 3x - y = 1 and 3x - y = 10.
Note: since we are about to find the area of the square, we simply find the length of any side using the distance formula between two parallel lines.
Further,
The two parallel sides are
x + 3y = 1 and x + 3y = 10
The required distance between them is
a = | 10 - 1 | / √(1² + 3²) units
= 9/√10 units
∴ the area of the square is
= 9/√10 × 9/√10 square units
= 81/10 square units
