how to find the altitude of a triangle
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 = (y2- y1)/(x2- 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 = (y2- y1)/(x2- 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 = (y2- y1)/(x2- 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
- How to prove if the given points are collinear using slope
- Conditions for collinearity
- Conditions for collinearity of three points
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how to find the altitude of a triangle
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