Thread: Circumcenter and Orthocenter of a triangle

Here's the orthocentre, roughly.

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

thank you so much for this

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

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

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.

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 $\displaystyle y=-\frac{21}{6}x+150.5$ and $\displaystyle y=20x-1013$

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).

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 $\displaystyle y=-\frac{21}{6}x+150.5$ and $\displaystyle y=20x-1013$

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

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.