Geometry

Question Analysis

The principal aim is to locate the orthocenter of the triangle defined by vertices , , and . This requires leveraging concepts of slopes, perpendicular lines, and line equations to find the intersection of the altitudes.

 

Key Concept Explanation

1. Slope formula: The slope  between two points  and  is .

2. Perpendicular lines: For two perpendicular lines with slopes  and , .

3. Point - slope form: The equation of a line passing through  with slope  is .

4. Orthocenter: The orthocenter of a triangle is the point of concurrency of its altitudes.

 

Step - by - Step Solution

1. Find slopes of triangle sides:

2. Determine slopes of altitudes:

Slope of altitude from  to : Since , the slope of this altitude

Slope of altitude from  to : Since , the slope of this altitude

Click "Show Answer" to reveal the answer and analysis