Question

Determine, graphically, the vertices of the triangle formed by the lines

y = x, 3y = x, x + y = 8

Answer 1

Given linear equations are

y = x …(i)

3y = x …(ii)

and x + y = 8 …(iii)

Table for line y = x,

Plotting the points A (1, 1), B(2,2), C (3, 1), D (6, 2), we get the straight lines AB and CD.

Similarly, plotting the point P (0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR.

AB and CD intersects the line PR on Q and D, respectively.

So, △OQD is formed by these lines. Hence, the vertices of the △OQD formed by the given lines are O(0, 0), Q(4, 4) and D(6,2).