Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.

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.

Then, 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

Thus, area of the triangle formed by the three given lines

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