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Given:

Lines xy = 0 and x + y = 1

To find:

The coordinates of the orthocenter of the triangle formed by the lines xy = 0 and x + y = 1

Explanation:

The equation xy = 0 represents a pair of straight lines.

The lines can be written separately in the following way:

x = 0 … (1)

y = 0 … (2)

The third line is

x + y = 1 … (3)

Lines (1) and (2) are perpendicular to each other as they are coordinate axes.

Therefore, the triangle formed by the lines (1), (2) and (3) is a right-angled triangle.

Thus, the orthocentre of the triangle formed by the given lines is the intersection of x = 0 and y = 0, which is (0, 0).

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