**How to find slope of altitude of a triangle :**

Here we are going to see how to find slope of altitude of a triangle.

In the above triangle the line AD is perpendicular to the side BC, the line BE is perpendicular to the side AC and the side CF is perpendicular to the side AB.

The sides AD, BE and CF are known as altitudes of the triangle.

Since the sides BC and AD are perpendicular to each other, the product of their slopes will be equal to -1

Slope of AD = -1/Slope of BC

Slope of BE = -1/Slope of AC

Slope of CF = -1/Slope of AB

Let us look into some example problems based on the above concept.

**Example 1 :**

The vertices of a triangle ABC are A(1 , 2), B(-4 , 5) and C(0 , 1). Find the slopes of the altitudes of the triangle.

**Solution :**

**Slope of BC :**

m = (y_{2 }- y_{1})/(x_{2 }- x_{1})

B (-4, 5) and C (0, 1)

m = (1 - 5)/(0-(-4))

= -4/(0 + 4)

= -4/4

= -1

Slope of AD = -1/Slope of BC

= -1/(-1)

= 1

**Slope of AC :**

m = (y_{2 }- y_{1})/(x_{2 }- x_{1})

A (1, 2) and C (0, 1)

m = (1 - 2)/(0-1)

= -1/(-1)

= 1

Slope of BE = -1/Slope of AC

= -1/1

= -1

**Slope of AB :**

m = (y_{2 }- y_{1})/(x_{2 }- x_{1})

A (1, 2) and B (-4, 5)

m = (5 - 2)/(-4 - 1)

= 3/(-5)

= -3/5

Slope of CF = -1/Slope of AB

= -1/(-3/5)

= 5/3

Hence the slopes of AD, BE and CF are 1, -1, and 5/3.

- How to prove if the given points are collinear using slope
- Conditions for collinearity
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After having gone through the stuff given on "How to find slope of altitude of a triangle", we hope that the students would have understood how to solve problems using unit rates.

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