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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8