What is the orthocenter of a triangle with corners at #(5 ,7 )#, #(2 ,3 )#, and #(7 ,2 )# ?
1 Answer
Explanation:
Orthocenter of a triangle is a point where the three altitudes of a triangle meet. To find the orthocentre, it would be enough, if intersection of any two of the altitudes is found out. To do this, let the vertices be identified as A(5,7), B(2,3), C(7,2).
Slope of line AB would be
Now consider the slope of line BC, it would be
Now eliminating y from the two equations of altitudes , by subtracting one eq from the other it would be
The orthocentre is thus