First slide
Cartesian plane
Question

If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x + y = 1, then the orihocenire of the triangle is

Moderate
Solution

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=23

So, the coordinates of Hare

23cosπ4,23sinπ4(1/3,1/3)

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