Triangle abc has vertices A(0,0), B(0,-2), C(-3,0) what is the orthocenter

Question

I need help. I dont understand the problem at all

Answer 1

Katherine,

 

This is an easy problem once you understand what an orthocenter is.  

 

First recall that an altitude line in any triangle from any vertex meets the opposite side at a right angle. Depending on the triangle's shape, that altitude line may lie either inside or outside the triangle as the opposite side has to be extended to get a right angle.  Since a triangle has 3 vertices, it has 3 corresponding altitudes.

 

Where these 3 altitudes all cross is defined as the orthocenter.  The prefix "ortho" means perpendicular and refers to the altitudes that are drawn from each vertex. Center means they all cross at a single point. That point will be somewhere inside the triangle for most triangle shapes, but can be outside for some weird obtuse triangle for example.

 

In your case, you have a right triangle in quadrant III with 2 sides on the axes.  Side AC is on the minus x-axis and side AB is on the minus y axis.  These sides meet at a right angle at the origin, and so are already altitudes of vertices B and C.  The altitude for vertex A also goes thru the origin and crosses the hypotenuse in a right angle.

 

So all 3 altitudes cross each other at vertex A(0,0), so point A is the orthocenter for this triangle.