SOLUTION: The sides of a triangle lie along the straight line with equations y=1; x+y=6 and y-3x+2=0. (a) Find the equation of the altitudes. (An altitude is a line through a vertex perpend

Question 1107299: The sides of a triangle lie along the straight line with equations y=1; x+y=6 and y-3x+2=0.
(a) Find the equation of the altitudes. (An altitude is a line through a vertex perpendicular to the opposite)
(b) Show that the altitudes are con-current and find the coordinates of the point where they meet (the point is called the orthocentre of the triangle).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

a) The vertices are
, given by
--> --> ,
, given by
--> --> --> , and
, given by
--> --> --> --> --> .
Side is the horizontal line .
The altitude from to , perpendicular to
is the vertical line
Side is the line <--> , with slope .
The altitude from to , perpendicular to
having slope , is
--> --> .
Side is the line <--> , with slope .
The altitude from to , perpendicular to
having slope , is
--> --> --> .

The intersection of and is given by
--> .
The intersection of and is the solution to
--> --> --> ,
also point .
The intersection of and is the solution to
--> --> --> --> --> ,
also point .
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