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,

x	0	1	2
y	0	1	2

Table for line x = 3y,

x	0	3	6
y	0	1	2

Table for line x + y = 8

x	0	4	8
y	8	4	0

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, ΔOQD is formed by these lines.

Hence, the vertices of the ΔOQD formed by the given lines are O(0, 0), Q(4, 4) and D(6, 2).