# HOW TO FIND THE ALTITUDE OF A TRIANGLE WITH COORDINATES

## About "How to find the altitude of a triangle with coordinates"

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.

## Slopes of altitude

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- y1)/(x- x1)

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- y1)/(x- x1)

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- y1)/(x- x1)

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.

## Related topics

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.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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