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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