I have a problem with finding the center coordinates of each side in an equilateral triangle. I've linked an image below that shows exactly which coordinates I'm after.
I understand that I can work out the height of then triangle by using pythagoras theorem. I can split the triangle down the middle and calculate the opposite of one of the triangles.
However, I can't figure out how to work out the coordinates marked with a "?"
Is there any formula I can use to work this out? The center part of the triangle would be it's origin at (0,0) and the sides would be 3 units each.
Thankyou
Best Answer
The height of the equilateral triangle is $$h={\sqrt 3 \over 2}a$$
(you have $a=3$), and coordinates of its vertices are
$$A = \left(-\frac a 2, -\frac h 3\right),\quad B = \left(\frac a 2, -\frac h 3\right),\quad C = \left(0, {\frac 2 3}h\right).$$
The center of AC is ${A+C \over 2}$, the center of BC is ${B+C \over 2}$.