Q. 125.0( 4 Votes )

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Answer :

Given:


A(2, 3), B(4, -1) and C(1, 2).


To find:


The equation and the length of the altitude from the vertex A.


Concept Used:


Distance of a point from a line.


Explanation:


Equation of side BC:



x + y – 3 = 0


The equation of the altitude that is perpendicular to x + y – 3 = 0 is x – y + λ = 0.


Line x – y + λ = 0 passes through (2, 3).


2 – 3 + λ = 0


λ = 1


Thus, the equation of the altitude from the vertex A (2, 3) is x – y + 1 = 0.


Let d be the length of the altitude from A (2, 3).


d


d


Hence, the required distance is.


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