The equations of the given lines are
y – x = 0 ………………………… (1)
x + y = 0 ……………………….. (2)
x – k = 0 ……………………..… (3)
The point of intersection of lines (1) and (2) is given by
x = 0 and y = 0
The point of intersection of lines (2) and (3) is given by
x = k and y = –k
The point of intersection of lines (3) and (1) is given by
x = k and y = k
Thus, the vertices of the triangle formed by the three given lines are (0, 0), (k, –k), and (k, k).
We know that the area of a triangle whose vertices are (x1, y1), (x2, y2), and (x3, y3) is
Therefore, area of the triangle formed by the three given lines
