Posted by kelly on Monday, April 20, 2009 at 9:04pm.
There are 4 centres of a triangle,
the centroid, the orthocentre, the circumcentre and the incentre.
of those four you asked for the hardest one to find, lol
By definition, the incentre is the point in a triangle which is equidistant from each of the three sides
Are you familiar with the formula for finding the distance from a given point to a given line?
The distance from (p,q) to the line Ax + By + C = 0
= |Ap +Bq + C|/√(A^2+B^2)
so find the equation of each of the 3 sides of the triangle and write them in the general form
Ax+By+C=0
then using your given point, find 3 different expressions for the distance.
They must all be equal.
form 2 equations by setting any two of the expressions equal to each other.
That will give you 2 equations containing p and q.
solve.
Good luck, this is usually a very messy problem unless it was carefully planned.
(If somebody has a better way to do this, I would appreciate letting me know)
The general form of the equations are (4/3)x+y=(1688/3)
(-9/40)x+y=(19577/40)
(5/12)x+y=(-3929/12)
but then when I use the incenter(p,q)and express it for distance and set the equations equal to each other i get different things when I set the first 2 equations together than I do the second 2 and the first and last. Can you tell me what I am doing wrong?