In the triangle ABC with vertices A (2, 3), B (4, 1) and C (1, 2), find the equation and length of altitude from the vertex A.

Explanation

Let AD be the altitude of triangle ABC from vertex A. Accordingly,` AD ⊥ BC`


The slope of` BC = (2 + 1) / (1 - 4) = 3/(-3) = -1.`


Since AD is perpendicular to BC, the slope of` AD = -1 / (slope of BC) = -1/(-1) = 1.`


The equation of the line passing through point` (2, 3)` and having a slope of 1 (equation of AD) is


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