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Two vertices of a triangle are (4,-3) and (-2,5), if the orthocenter of the triangle is (1,2). Find the coordinates of the third vertex.

Two vertices of a triangle are (4,-3) and (-2,5), if the orthocenter of the triangle is (1,2). Find the coordinates of the third vertex.

Grade:12

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
let A=(4,-3) B=(-2,5) and orthocentre O=(1,2)
slope of altitude coming from A =\frac{-3-2}{4-1}=\frac{-5}{3}
BC slope =3/5(as it is perpendicular to altitude coming from A)
Equation of line through BC is y=(3/5)x+c
substituting (-2,5) in above eqn we get c=31/5
so equation is 5y=3x+31........(1)
similarly altitude coming from B slope=\frac{5-2}{-2-1}=-1
AC slope =1
Equation of AC is y=x+c
substituting A(4,-3) we get
c=-7
equation is y=x-7.....(2)
solving (1) and (2) we get third vertex as (33,26)
Thanks and Regards
Shaik Aasif
askIITians Faculty
sagar kumar
11 Points
6 years ago
assume the vertex to be determine as (p,q) then wrute down the equation of side of triangle from given vertices and equate the foot of perpendicular from orthocenter and (p,q) on the equation of side determined .from here we will get p and q.

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