Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
To find the orthocenter of triangle ABC, follow these steps:
1. Plot the points A(0, 6), B(4, 6), and C(1, 3) on a coordinate graph.
- Mark point A at coordinates (0, 6).
- Mark point B at coordinates (4, 6).
- Mark point C at coordinates (1, 3).
2. Draw the three sides of the triangle using line segments AB, BC, and CA.
- Connect point A to B with a straight line segment.
- Connect point B to C with another straight line segment.
- Connect point C back to point A with a final straight line segment.
3. Draw the altitudes of the triangle from each vertex.
- Drop a perpendicular line from point A to the opposite side BC.
- Drop a perpendicular line from point B to the opposite side AC.
- Drop a perpendicular line from point C to the opposite side AB.
4. The intersection point of all three altitudes is the orthocenter of the triangle.
- Label the intersection point as H. This is the orthocenter of triangle ABC.
Note: In the given example, the orthocenter of triangle ABC is not provided. You will have to plot the given points, draw the altitudes, and find their intersection to determine the orthocenter accurately.