Question

ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter including any necessary points or slopes you had to derive.

Answer 1

 Plot the points and draw the triangle. Now you have to draw a line that passes through a point, perpendicular to the triangle side that it's opposite from. Then do that again with a second point. The intersection of these two points will give you the Orthocenter. (You don't need to do it for the third point; it will pass through it anyway, but you only need two intersecting lines to define a point!) Since AB is a horizontal line, it will probably be easiest to start with the line perpendicular to AB that passes through C. You'll find that this is just the vertical line x=1. Now just pick another point and do it again. (Hint: if you know two points, you can find their slope, and you know that lines perpendicular to each other have negative reciprocal slopes.)