Given 2 vertexes and orthocenter, find the third vertex

[HuMoDz]

Vertexes: A(5,6) B(-1,-2) C(unknown)

Orthocenter: H(-1,2)

 

I've though this:

Find the line AB that crosses A and B -> Line HC that crosses H and C are perpendicular to it; use H to find its c (ax + by + c = 0) or q (y = mx + q)

But still, i don't know how to find C, only a line that passes through it

 

Help?:\

[imatfaal]

ok - so it is pretty simple to find using a straight edge and a compass. now I gotta think about how to get it analytically. perhaps you could try the straight edge and compass idea to get an idea of the arrangements

 

Humodz

 

there is almost certainly a quicker way - but this works (but no I am not giving you solution - just ideas)

 

1. Draw a diagram - everything looks better with a diagram

2. I am gonna assume that you can work out an equation for a straight line basis the slope and one point and basis two points

3. You know one line straight off - the line ab

4. You know the angle of the line hc with respect to the line ab (ie its an orthocentre) - with point and slope you know line hc

5. You also have two points each on the lines ah and bh - so you know those lines too

6. You know angle line ac makes with extension of line bh (ie its an orthocentre)

7. Ditto line bc

8. You know the three lines that make up abc

9. sorted

 

But really - do draw a diagram first off with all these problems