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Asked by Radha Last Modified
Answer 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
The perpendicular distance (d) of a line Ax + By + C = 0 from a point (x1, y1) is given by
.
On comparing equation (1) to the general equation of line Ax + By + C = 0, we obtain A = 1, B = 1, and C = –3.
∴Length of AD 
Thus, the equation and the length of the altitude from vertex A are y – x = 1 and 
units respectively.
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