Graph of Lines and Area of the Figure Formed

Video Explanation

Question

Draw the graphs of the lines \(x = -2\) and \(y = 3\). Write the vertices of the figure formed by these lines, the x-axis and y-axis. Also, find the area of the figure.

Solution

Step 1: Description of the Given Lines

The equation \(x = -2\) represents a straight line parallel to the y-axis.

The equation \(y = 3\) represents a straight line parallel to the x-axis.

The x-axis is given by \(y = 0\) and the y-axis by \(x = 0\).

Step 2: Graphical Representation

Draw the lines:

• \(x = -2\)
• \(y = 3\)
• x-axis \((y = 0)\)
• y-axis \((x = 0)\)

These four lines enclose a rectangular region.

Step 3: Vertices of the Figure

The vertices of the rectangle are obtained by pairwise intersections:

• Intersection of \(x = -2\) and \(y = 0\) → (−2, 0)
• Intersection of \(x = 0\) and \(y = 0\) → (0, 0)
• Intersection of \(x = 0\) and \(y = 3\) → (0, 3)
• Intersection of \(x = -2\) and \(y = 3\) → (−2, 3)

Step 4: Area of the Figure

Length of the rectangle = distance between x = −2 and x = 0 = 2 units

Breadth of the rectangle = distance between y = 0 and y = 3 = 3 units

\[ \text{Area} = \text{Length} \times \text{Breadth} = 2 \times 3 = 6 \]

Answer

Vertices of the figure are:

• (−2, 0)
• (0, 0)
• (0, 3)
• (−2, 3)

Area of the figure = 6 square units.

Conclusion

By drawing the graphs of the given lines along with the coordinate axes, a rectangle is obtained whose area is 6 square units.