Q. 124.8( 4 Votes )

Three sides AB, B

Answer :

Given:


The sides AB, BC and CA of a triangle ABC are as follows:


5x − 3y + 2 = 0 … (1)


x − 3y − 2 = 0 … (2)


x + y − 6 = 0 … (3)


To find:


The equation of the Altitude through the vertex A.


Concept Used:


Point of intersection of two lines.


Explanation:


Solving (1) and (3):


x = 2 , y = 4



Thus, AB and CA intersect at A (2, 4).


Let AD be the altitude.


ADBC


Slope of AD × Slope of BC = −1


Here, slope of BC = slope of the line (2) = 1/3


Slope of AD×1/3 = - 1 Slope of AD = - 3


Hence, the equation of the altitude AD passing through A (2, 4) and having slope −3 is y - 4 = - 3x - 2 3x + y = 10


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