Geometry

Question Analysis

The primary goal is to locate the orthocenter of the triangle with vertices , , and . We do so by calculating slopes of the triangle's sides, slopes of altitudes, constructing altitude equations, and finding their intersection.

 

Key Concept Explanation

1. Slope formula: Given  and , .

2. Perpendicular lines: If two lines with slopes  and  are perpendicular, .

3. Point - slope form:  helps find line equations.

4. Orthocenter: It’s the intersection of a triangle's altitudes.

 

Step - by - Step Solution

1. Find slopes of triangle sides:

Slope of : Given  and , .

Slope of : Given  and , .

Slope of : Given  and , .

2. Determine slopes of altitudes:

Slope of altitude from  to : Since

Click "Show Answer" to reveal the answer and analysis