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

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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...
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The equations of the given lines are

yx = 0 … (1)

x + y = 0 … (2)

xk = 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

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