Question

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

Answer 1

orthocentre of a triangle is the point of intersection of its 3 altitudes. A and B denote the 2 given vertices.
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 :)

Answer 2

Step-by-step explanation:

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