Question

ABC has vertices A(0, 6), B(4, 6), and 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

Answer:

  (1, 5)

Step-by-step explanation:

The graph is quite informative. It shows that line BC has a slope of 1, so the altitude from point A to that line has a slope of -1. Line AB is horizontal, so the altitude from C to that line is the vertical line x=1. The two lines intersect at the orthocenter, (1, 5).

Steps:

1. draw the triangle
2. draw the altitude line from vertex C
3. notice the slope of BC is 1
4. draw the altitude line from vertex A with slope -1
5. note the point of intersection of the lines: (1, 5), the orthocenter