Find the coordinates of the orthocenter of Triangle A B C with vertices ALeft-parenthesis 2 comma 6 right-parenthesis, BLeft-parenthesis 8 comma 6 right-parenthesis, and CLeft-parenthesis 6 comma 2 right-parenthesis.
A. Left-parenthesis 5 comma 4 right-parenthesis
B. Left-parenthesis 1 comma 2 right-parenthesis
C. Left-parenthesis 6 comma 4 right-parenthesis
D. Left-parenthesis 6 comma 8 right-parenthesis
2 answers
A. Left-parenthesis 5 comma 4 right-parenthesis
Why not just say A(2,6) , B(8,6) and C(6,2)
we need the intersection of altitudes.
since AB is horizontal, x = 6 is the altitude from C to AB
Slope of AC = -1, so slope of altitude from B to AC = +1
equaltion of that altitude: y = x + b
(8,6) lies on it
6 = 8 + b , b = -2
altitude from B to AC is y = x - 2
but x = 6
then y = 6-2 = 4
the orthocentre is (6,4)
we need the intersection of altitudes.
since AB is horizontal, x = 6 is the altitude from C to AB
Slope of AC = -1, so slope of altitude from B to AC = +1
equaltion of that altitude: y = x + b
(8,6) lies on it
6 = 8 + b , b = -2
altitude from B to AC is y = x - 2
but x = 6
then y = 6-2 = 4
the orthocentre is (6,4)