Question

Draw the graphs of the following linear equations on the same graph paper. 

2x + 3y = 12, x – y = 1 

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.

Answer 1

x - y = 1 

2x + 3y = 12 

2x + 3y = 12 passes through (6, 0) and (0, 4) 

x – y = 1 passes through (1, 0) and (0, -1)

Coordinates of the vertices of the triangle formed with the y axis are (0, 4), (0, -1) and (3, 2) 

Base of the triangle = 4 + 1 = 5 

Height of the triangle = 3 

Area of the triangle = \(\frac{1}{2}\) x base x height

⇒ Area of the triangle = \(\frac{1}{2}\) x 5 x 3