I searched through the forum and found some threads about this, but it seems like I'm doing everything right but I'm getting an unreasonable answer that doesnt seem right when i match it up with the coordinate i drew before hand
The problem: Triangle ABC with X(73,33) Y(33,35), and Z(52,27), find the circumcenter and Orthocenter of the triangle.
Here is what i did for circumcenter. I found the slope of XY which is -2/40 so the perp slope is 20. The slope of XZ is 6/21 so the perp slope is -21/6.
Then i found the midpt of XY and I got (53,34) and named it as point A. Next, the midpt of XZ is (62.5,30) and I named it B.
And then i set up these two formulas: y = 20x - 1026 (i found the y-intercpt using point A), and y = -21/6x + 248.75 (using pt E).
Then I set up a system: x-4 = 5x+24 and got x=54.245 and substituted it for the first formula and got y=58.9. So i got (54.245,58.9) as the answer.
I tried to match it up but the answer i got, the point was way off, what am i doing wrong? is it the calculations cuz i checked it like 3 times?
Here is what i did for orthocenter. I found the slope of XY which is -2/40 so the perp slope is 20. The slope of XZ is 6/21 so the perp slope is -21/6
Then i used the formulas: y= 20x-1013 (the XY altitude that contains the point Z) and y=-21/6x+150.5(the XZ altitude that contains the point Y).
Then I set up a system: 20x-1013 = -21/6x+150.5 and got x= 49.511 and substituted it for the first formula and got y=22.78. So i got (49.511,22.78) as the answer.
and also like the circumcenter I tried to match it up with the point i contructed using a compass before hand but the point is still off?? why? what am i doing wrong?
any help is appretiated. i am so confused
Hi, fuyu1993,
Your circumcentre looks fine.
Check your calculations for verifying it.
If it's the centre of a circle, then it has to be the same distance from
all 3 given points.
You can use Pythagoras' theorem for that.
Alternatively, you may verify that the point you found lies on all 3 perpendicular bisectors by placing the x and y you worked out into all 3 equations for the bisectors and verifying that the equations are true for those co-ordinates.
You have made an error calculating the orthocentre.
You have miscalculated when solving the equations of the perpendicular lines that passes through the opposite vertices.
for the circumcenter, when i use a compass to constuct, i got the coordinate (54,35) with some decimals and it is the same distance to all 3 points but my calculations seems not to match up with my constuction. why? =[
i cant find the error for orthocentre, i checked like 5 times and eveytime it came out with the same answer that dont match my construction
sorry for so many questions and mt bad english , i am really confused about this.