# Thread: Circumcenter and Orthocenter of a triangle

1. Here's the orthocentre, roughly.

You wrote y=22.78 instead of -22.78 for this.

2. thank you so much for this

3. Originally Posted by Archie Meade
Here's the orthocentre, roughly.

You wrote y=22.78 instead of -22.78 for this.
the point on the picture is like (51,-18), it doesnt match with my calculations, can u explain how to do it the right way? if it's not too much trouble? thx

4. You had earlier, the equation $y=-\frac{21}{6}x+150.5$

For x=49.5, this is -21(8.2)+150.5=-172.2+150.5=-21.7 approx

My diagram is not carefully done,
it looks like y is about -18, but it would be correct, if i'd taken more time to draw a very accurate sketch.

5. To verify your calculations, place the co-ordinates of the orthocentre into the equations of the perpendicular lines.
The orthocentre is a point on both of the perpendiculars, which contain the opposite vertex (actually all 3 perpendiculars).

If you calculate the orthocentre correctly,
which you did except for having the sign on the y co-ordinate wrong,
you should now be able to place x=49.5 into both $y=-\frac{21}{6}x+150.5$ and $y=20x-1013$

and get the exact same y=-22 approx for both.

Or you could use y and find that you get the same x=49.5 for both
(or all 3 perpendiculars, if you formulate the 3rd one).

6. Originally Posted by Archie Meade
To verify your calculations, place the co-ordinates of the orthocentre into the equations of the perpendicular lines.
The orthocentre is a point on both of the perpendiculars, which contain the opposite vertex (actually all 3 perpendiculars).

If you calculate the orthocentre correctly,
which you did except for having the sign on the y co-ordinate wrong,
you should now be able to place x=49.5 into both $y=-\frac{21}{6}x+150.5$ and $y=20x-1013$

and get the exact same y=-22 approx for both.

Or you could use y and find that you get the same x=49.5 for both
(or all 3 perpendiculars, if you formulate the 3rd one).
thanks you so much, i think i get it now.
ima try to draw it myself

7. When you draw hand sketches, normally the co-ordinates will be a little bit
off, since you'd have to draw extremely accurately.

Solving the equations is very exact, though it's best to write
the x and y co-ordinates of the centres as fractions rather than decimals.

Practice and you'll improve fast.
Circumcentre and orthocentre are good for mastering line equations.

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