If two vertices of a triangle are and , orthocentre lies at the origin and centroid on the line , then the third vertex lies at

a)

(7, 4)

b)

(8, 14)

c)

(12, 21)

d)

None of these

1 Answer

127 votes

Answer Key / Explanation : (d) -

(d)

Given is the orthocentre. Let be the third vertex, and the other two vertices. Then the slope of the line through and is , while the lines through and has the slope . By the property of the orthocenter, these two lines must be perpendicular, so we have