SOLUTION: Okay I have to find the orthocenter of a triangle with the coordinates of P(2,5) Q(8,5) and R(8,1). If you map it out you get one horizontal side and one vertical side... A right t

Question 1065320: Okay I have to find the orthocenter of a triangle with the coordinates of P(2,5) Q(8,5) and R(8,1). If you map it out you get one horizontal side and one vertical side... A right triangle. My math teacher doesn't know how to teach. Please help me find the orthocenter. It's due tomorrow.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Find the equation for the line perpendicular to line PQ, containing point R.

Find the equation for the line perpendicular to line QR, containing point P.

These two equations intersect at the triangle's orthocenter.

To be more complete, also find the equation of the line perpendicular to line PR, containing point Q. All three found lines should intersect at the orthocenter.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.
Okay I have to find the orthocenter of a triangle with the coordinates of P(2,5) Q(8,5) and R(8,1).
If you map it out you get one horizontal side and one vertical side... A right triangle. My math teacher doesn't know how to teach.
Please help me find the orthocenter. It's due tomorrow.
~~~~~~~~~~~~~~~~~~~~~~`

Nothing can be easier.

For this right-angled triangle, as for ANY right-angled triangle, the ORTHOCENTER is the right angle vertex.

------------------------

By the way, do you know what the ORTHOCENTER of a triangle is ?

It is the intersection point of all three altitudes of the triangle.

Useful notice: For any triangle, its altitudes are concurrent, which means that all three altitudes intersect at one point.

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