Question

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

Answer 1

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).