Question

Find the orthocentre of the triangle ABC formed by vertices A(1,5), B(2,6) and C(3,3)​

Answer 1

Given :  triangle ABC formed by vertices A(1,5), B(2,6) and C(3,3)​

To Find : orthocentre of the triangle

Solution:

orthocentre of the triangle  - where altitude of triangle meets

A(1,5), B(2,6) and C(3,3)​

Slope of  AB  (6 - 5)/(2 - 1)  = 1

Slope of altitude passing through vertex C = - 1

y - 3 = -1(x - 3)

=> x + y = 6  

Slope of  AC  (3 - 5)/(3 - 1)  = -1

Slope of altitude passing through vertex B =  1

y - 6 =  (x - 2)

=> x - y  = - 4

x + y = 6  

x - y  = - 4

on solving

=> x = 1   ,  y = 5

orthocentre of the triangle ABC formed by vertices A(1,5), B(2,6) and C(3,3)​ is ( 1, 5)

Point A ( 1, 5) is orthocentre

Means given triangles is right angle at A

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