Thread: Orthocenter...what is it with this triangle

Whats the orthocenter of a triangle with coordinates R (-1 , -4) , P (-1 , 5) , Q (7 , 2).

Please show how you did it as simple as possible

Thanks

Originally Posted by squat4speed

Whats the orthocenter of a triangle with coordinates R (-1 , -4) , P (-1 , 5) , Q (7 , 2).

Please show how you did it as simple as possible

Thanks

i think you need to find the midpoint of the 2 sides of the triangle. from these new points you will come up with 2 equation (linear equation) and find the coordinates of the point of intersection. that would be your orthocenter..
i hope this is correct...

how do i find coordinates of point of intersection

Alright I got a head ache..and im confusing myself somehow, can someone please give me a step by step show of how you find the coordinates of the orthocenter.

Originally Posted by squat4speed

how do i find coordinates of point of intersection

when you got 2 equation what you need to do is solving using simultaneous or substitution method.

first draw your triangle.
ok i got midpoint of RQ=(3,-1) <<---let this point be point A
and PR=(-1,1/2)<<-------- this point be point B

now find the equation of line that passes through point B and point Q (first equation)
and equation of line that passes through A and P(second equation).

Hello, squat4speed!

What's the orthocenter of a triangle with coordinates:

The orthocenter is the intersection of the three altitudes of the triangle.

Find the equation of two of the altitudes and locate their intersection.

If you make a sketch, the problem is much simpler.

Code:

          P   |
    (-1,5)*   |
          * * |
          *   *
          *   | *
          *   |   *
          *   |     *
      - - * - + - - - *Q
          *   |     * (7,2)
          *   |   *
    ------*---+-*----------
          *   *
          * * |
   (-1,-4)*   |
          R   |
              |

Side is vertical.
Hence, the altitude from is the horizontal line, .[1]

Side QR has slope: .

Hence, the altitude from has slope
Its equation is: . .[2]

The intersection of [1] and [2]: .


Therefore: .

The orthocenter is: .

if you draw on the graph paper you will get (1.6,1)