Question

if origin is the orthocenter of triangle abc where A(5,-1),B(-2,3) then the orthocentre of triangle OAC

Answer 1

if origin is the orthocenter of triangle abc where A(5,-1),B(-2,3) then the orthocentre of triangle OAC

• Given,
• the vertices of triangle are,
• A(5,-1), B(-2,3)
• and the orthocenter is O(0,0)
• Using the property of triangles, we have, "If O is orthocentre of triangle ABC then the four points O, A, B, C are such that each point is orthocentre of the triangle formed by other three points."
• If one of the vertices of a triangle is origin, with remaining vertices (x1,y1) and (x2,y2),  then orthocentre is ( k{y1-y2} , k{x1-x2} )  
• ∴ C = (-1 - 3, 5 - ( -2 ) )
• C= (-4, 7)

Answer 2

if origin is the orthocenter of triangle abc where A(5,-1),B(-2,3) then the orthocentre of triangle OAC

Given,

the vertices of triangle are,

A(5,-1), B(-2,3)

and the orthocenter is O(0,0)

Using the property of triangles, we have, "If O is orthocentre of triangle ABC then the four points O, A, B, C are such that each point is orthocentre of the triangle formed by other three points."

If one of the vertices of a triangle is origin, with remaining vertices (x1,y1) and (x2,y2),  then orthocentre is ( k{y1-y2} , k{x1-x2} )  

∴ C = (-1 - 3, 5 - ( -2 ) )

C= (-4, 7)