**How to find the altitude of a triangle with coordinates :**

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.

**Question 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
- Conditions for collinearity of three points

After having gone through the stuff given on "How to find the altitude of a triangle with coordinates", we hope that the students would have understood how to solve problems using unit rates.

Apart from the stuff given above, if you want to know more about "How to find the altitude of a triangle with coordinates", please click here

Apart from the stuff given on "How to find slope of altitude of a triangle", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...