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Question
Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.
Solution
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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