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orthocenter question!!?
the vertices of triangle DEF are D(4,0), E(-2,4) and F(0,6). Find the coordinates of the orthocenter of triangle DEF.
I need to show my work.. i have no idea how to!!!
1 Answer
- dennisLv 69 years agoFavorite Answer
Your triangle is isosceles DE = DF = sqrt 52
The orthocenter is the point of intersection of the 3 altitudes.
The altitude from D to EF joins D to the midpoint of of EF (since the triangle is isosceles) which is (-1 , 5) so its equation is
y - 0 = m( x - 4 ) where m = 5/-5 = - 1 so we have y = - x + 4 .......(1)
We now work out the equation of the altitude from F to ED
Gradient of ED is 4/ - 6 = - 2/3 so gradient of altitude is 3/2 and it passes through (0,6)so its equation is
y = (3/2)x +6 .......(2)
Solve (1) and (2) to get the coordinates of the orthocenter. (- 4/5 , 24/5)
