How to calculate the altitude of a triangle using coordinate geometry principles
In short: When a triangle's base is not horizontal or vertical, finding its altitude requires understanding perpendicular lines. This video explains how to determine the equation of the line containing an altitude by leveraging the relationship between opposite reciprocal slopes.
In coordinate geometry, the altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Because this altitude is perpendicular to the base, its slope is the opposite reciprocal of the base's slope.
By identifying the slope of the base on a coordinate plane, you can derive the equation for the altitude line. This method is a standard application of coordinate geometry, frequently taught in secondary education curricula such as the Texas TEKS.
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Sources
- Summary by Intellect · source: Triangle altitude equation | Coordinate geometry | Geometry (TX TEKS) | Khan Academy
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