Which process is used to find the equation of an altitude from a vertex in a triangle?

To find the equation of an altitude from a vertex in a triangle, one effective method is to determine the slope of the side opposite to the vertex and then find the negative reciprocal of that slope.

An altitude in a triangle is a line segment that extends from a vertex perpendicular to the line containing the opposite side. Since two lines are perpendicular if the product of their slopes is -1, finding the negative reciprocal of the slope of the opposite side provides the slope of the altitude.

Once the slope of the altitude is found, it can be combined with the coordinates of the vertex from which the altitude is drawn to write the equation of the altitude in point-slope form or slope-intercept form. This process is fundamental in geometric proofs and constructions, allowing for the derivation of various properties within triangles, such as determining the orthocenter or understanding the relationships between angles and sides.

Other options, while they may relate to different aspects of triangle geometry, do not specifically address the process needed for finding the altitude's equation. For instance, calculating the area relates to finding the overall size of the triangle but not directly to altitude construction. Identifying a midpoint or using the distance formula would assist in different contexts but does not yield the altitude's equation specifically.