Questions
If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation, then the orihocenire of the triangle is
a
(1/3,1/3)
b
(2/3,2/3)
c
(2/ 3, 2/ 3)
d
none of these
detailed solution
Correct option is A
Let OAB be the equilateral triangle. In an equilateral triangle the orthocentre and centroid coincide. So, the orthocentre H divides OL in the ratio 2: 1. OL = Length of the L from (0, 0) on x + y -1= 0⇒ OL=12∴ OH=23×OL=23So, the coordinates of Hare23cosπ4,23sinπ4≡(1/3,1/3)Talk to our academic expert!
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If an triangle circumcentre and orthocentre then the coordinates of the midpoint of the side opposite to A are
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