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.
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Solution
Let AD be the altitude of triangle ABC from vertex A.
Accordingly, AD⊥BC
The equation of the line passing through point (2, 3) and having a slope of 1 is
(y – 3) = 1(x – 2)
⇒ x – y + 1 = 0
⇒ y – x = 1
Therefore, equation of the altitude from vertex A = y – x = 1.
Length of AD = Length of the perpendicular from A (2, 3) to BC
The equation of BC is
Concept: General Equation of a Line
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