Geometry

Question Analysis

The main focus is to determine the orthocenter of the triangle having vertices , , and . This requires calculating slopes of the sides, finding slopes of altitudes, formulating altitude equations, and identifying their intersection point.

Key Concept Explanation

1. Slope formula: For two points  and , .

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

3. Point - slope form:  is used to find the equation of a line.

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

Step - by - Step Solution

1. Calculate slopes of triangle sides:

Slope of : Given  and , . So,  is a horizontal line.

Slope of : Given  and , .

Slope of : Given  and ,

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