Hello,

Two lines of the first triangle (4x-7y+10=0 and 7x+4y=15) are perpendicular, making it a right-angled triangle. Its orthocentre is their point of intersection, which is (1, 2).

The second triangle (x=0, y=0, x+y=1) is also a right-angled triangle, and its orthocentre is the origin, (0, 0).

The distance between these two orthocentres, (1, 2) and (0, 0), is √(1-0)²+(2-0)² = √5.

Final Answer: √5.