I was helping my ds with math last night, but we went to bed tired and frustrated with these sorts of problems. I think we might have been okay with circumcenter, but not the other two. The book was not helpful on this. We plan to try again when fresher on Saturday morning.
1. Given triangle ABC with coordinates: A (-2,1) B (0, -2) C (5, -2) find the coordinates for the centroid, orthocenter, and circumcenter.
2. Given triangle ABC with coordinates: A (2, -3) B (3, 3) C (-1, -2) find same as in #1.
It seems like we need to be able to use: Point slope formula, (y-y1)=m(x-x1)
and then set two equations equal to each other to get the intersection.
E.g., by solving for two altitude equations, get the orthocenter ; or for two perpendicular bisector equations, get the circumcenter; or for two lines passing through 2 medians and 2 vertices get the centroid. But we can't seem to do it. We tried and came up with answers that clearly are wrong based on an approximation from drawing it on graph paper.
Are we on the right track as to what we think we need to do, and maybe were just too tired to do it? Or are we off track in what we are trying to do?