Q. 124.4( 5 Votes )

Find the equations to the altitudes of the triangle whose angular points are A (2, – 2), B(1, 1), and C ( – 1, 0).

Answer :

A triangle is given with three angular points A (2, – 2), B(1, 1), and C ( – 1, 0)

To Find: Find the equation.


Formula Used: The equation of line is (y – y1) = m(x – x1)



Explanation: Here, AD, BE and CF are the three altitudes of the triangle.


Now,


We know, The slope of the line with two points is, m =


So, The slope of BC =


The slope of AC =


The slope of AB =


and, The product of two slopes of the perpendicular line is always – 1


So, (slope of AB) × (slope of CF) = – 1


The slope of CF =


(slope of BE)×(slope of AC) = – 1


The slope of BE =


(slope of AD)×(slope of BC) = – 1


The slope of AD =


So, The equation of line is (y – y1) = m(x – x1)


The equation of Line AD is


y – ( – 2) = – 2(x – 2)


y + 2 = – 2x + 2


2x + y – 2 = 0


The equation of Line BE is



2y – 2 = 3x – 3


2y – 3x + 1 = 0


The equation of Line CF is



x – 3y + 1 = 0


Hence, The equation of the three equation is calculated.


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