Question

Please help!!!!

Find the coordinates of the orthocenter for triangle ABC. (Diagram in comments)

Answer 1

It may seem simple to you, but I am clueless when it comes to geometry.

Answer 2

nope

Answer 3

Orthocenter is intersection of altitudes, right? It's been a while since I've done these . . .

Answer 4

Yeah

Answer 5

Eh.. I'm sure there's an easier way using some theorem I can't remember right now, so my first instinct is to set up a system of equations using distance formula.

Answer 6

It's isosceles, so that simplifies things . . .

Answer 7

Right

Answer 8

Here's what I'm seeing now from the picture for the purpose of simplifying assumptions:
It's isosceles, so one altitude is going to go from B(6,6) to (6,0) because of symmetry.
Also because of symmetry, the other two altitudes are going to be equal in length.

Answer 9

And, for example, the altitude going from A(0,0) to side BC has to be perpendicular to that side, so you know that line has opposite-reciprocal slope to the line which contains BC.

Answer 10

Can you find it from there?

Answer 11

My first instinct seems unnecessary - distance formula isn't required, only the system of two lines to find the intersection point.

Answer 12

In fact, I think ganeshie8 was right, it is a right triangle, so the solution is trivial.

Answer 13

Trivial...okay. I think