Let the three side of triangle are on the line 4x - 7y 10 =0 X y= 5 and 7x 4y = 15 then the distance of it orthocentre from the orthocentre of the triangle formed by the lines X =0, y=0 and X y=one is
Answer (1)
11th Oct, 2025
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.
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