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 the y-axis. Also, find the area of the figure.

Answer 1

1. Graphical representation

The line x = –2 is a vertical line passing through x = –2 on the x-axis. 

The line y = 3 is a horizontal line passing through y = 3 on the y-axis.

The x-axis is the line y = 0.

The y-axis is the line x = 0.

2. Vertices of the figure

By finding the pairwise intersections of the four lines, we get the coordinates of the four vertices:

Origin (intersection of x-axis and y-axis): O(0, 0) 

Intersection of x = –2 and x-axis (y = 0): C(–2, 0) 

Intersection of x = –2 and y = 3: B(–2, 3) 

Intersection of y-axis (x = 0) and y = 3: A(0, 3)

3. Area of the figure

The enclosed region forms a rectangle. Its dimensions are calculated by finding the absolute lengths:

Length (along x-axis) = |0 – (–2)| = 2 units

Width (along y-axis) = |3 – 0| = 3 units

Area = Length × Width

= 2 × 3

= 6 square units