Answer :

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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