# Find the equation

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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