# Two vertices of a triangle are (3, - 2) and (-2,3) and it's orthocentre is (-6,1). then find the third vertex is?

1
by nikhil3

Log in to add a comment

by nikhil3

Log in to add a comment

find out the slope of AB.

now, AB is perpendicular to the altitude from C.

name the co-ordinates of C as (a,b).

find out the slope of CO where O denotes the orthocentre.

this slope is perpendicular to the slope of AB.

next, take the side, say AC, find its slope. then, find the slope of BO. These 2 slopes are perpendicular to each other and hence, have the product -1.

now, you have got 2 equations to solve for 2 variables which are a,b for the third vertex.

if you still have doubts, ask :)