HOW TO FIND THE EQUATION OF ALTITUDE OF A TRIANGLE

How to Find the Equation of Altitude of a Triangle ?

Here we are going to see, how to find the equation of altitude of a triangle.

How to Find the Equation of Altitude of a Triangle - Questions

Question 1 :

A(-3, 0) B(10, -2) and C(12, 3) are the vertices of triangle ABC . Find the equation of the altitude through A and B.

Solution :

Equation of altitude through A

Solution :

The altitude passing through the vertex A intersect the side BC at D.

AD is perpendicular to BC.

Slope of BC  =  (y2 - y1)/(x2 - x1)

  =  (3 - (-2))/(12 - 10)

  =  (3 + 2)/2

  =  5/2

Equation of the altitude passing through the vertex A :

(y - y1)  =  (-1/m)(x - x1)

A(-3, 0) and m = 5/2

(y - 0)  =  -1/(5/2)(x - (-3))

y = (-2/5) (x + 3)

5y  =  -2x - 6

2x + 5y + 6  =  0

Equation of altitude through B

Slope of AC  =  (y2 - y1)/(x2 - x1)

  =  (3 - 0)/(12 - (-3))

  =  3/(12+3)

  =  3/15

=  1/5

Equation of the altitude passing through the vertex B :

(y - y1)  =  (-1/m)(x - x1)

B(10, -2) and m = 1/5

(y - (-2))  =  -1/(1/5)(x - 10)

y + 2  =  -5(x - 10)

y + 2  =  -5x + 50

5x + y + 2 - 50  =  0

5x + y - 48  =  0.

Question 2 :

Find the equation of the perpendicular bisector of the line joining the points A(-4,2) and B(6,-4).

Solution :

Perpendicular bisector means, the line will pass through the midpoint of the line segment AB and makes an 90 degree angle.

midpoint  =  (x1 + x2)/2, (y1 + y2)/2

  =  (-4 + 6)/2, (2 - 4)/2

  =  2/2, -2/2

  =  (1, -1)

Slope of AB  =  (y2 - y1)/(x2 - x1)

=  (-4-2)/(6+4)

=  -6/10

=  -3/5

Equation of perpendicular bisector :

(y - y1)  =  (-1/m)(x - x1)

(y + 1)  =  (5/3)(x - 1)

3(y + 1)  =  5(x - 1)

3y + 3  =  5x - 5

5x - 3y - 5 - 3  =  0

3x + 5y - 8  =  0

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Equation of Altitude of a Triangle". 

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