HOW TO FIND THE SLOPES OF MEDIAN AND ALTITUDE OF A TRIANGLE

How to Find the Slopes of Median and Altitude of a Triangle :

Here we are going to see how to find the slopes of median and altitude of a triangle.

How to Find the Slopes of Median and Altitude of a Triangle - Examples

Question 13 :

A triangle has vertices at (6 , 7), (2 , -9) and (-4 , 1). Find the slopes of its medians.

Solution :

Median drawn through the vertex A will pass through the midpoint of the side BC.

Midpoint of BC  =  D

Midpoint  =  (x1 + x2)/2, (y1 + y2)/2

B(2, -9) and C(-4, 1)

=  (2 - 4)/2, (-9 + 1)/2

=  -2/2, -8/2

=  D(-1, -4)

Slope of the median AD :

A(6, 7) D(-1, -4)

=  (y2 - y1)/(x2 - x1)

=  (-4 - 7) / (-1 - 6)

=  -11/(-7)

=  11/7

Slope of the median AD  =  11/7.

Median drawn through the vertex B will pass through the midpoint of the side AC.

Midpoint of AC  =  E

A(6, 7) and C(-4, 1)

=  (6 - 4)/2, (7 + 1)/2

=  2/2, 8/2

=  E(1, 4)

Slope of the median BE :

B(2, -9) E(1, 4)

=  (y2 - y1)/(x2 - x1)

=  (4 + 9)/(1 - 2)

=  13/(-1)

Slope of the median BE  =  -13

Median drawn through the vertex C will pass through the midpoint of the side AB.

Midpoint of AB  =  F

A(6 , 7) and B(2 , -9)

=  (6 + 2)/2, (7 - 9)/2

=  8/2, -2/2

=  F (4, -1)

Slope of the median CF :

C (-4 , 1) F (4, -1)

=  (y2 - y1)/(x2 - x1)

=  (-1 - 1)/(4 + 4)

=  -2/8

Slope of the median CF  =  -1/4

Question 14 :

The vertices of a triangle ABC are A(-5 , 7), B(-4 , -5) and C(4,5). Find the slopes of the altitudes of the triangle.

Solution :

Every altitude drawn through the vertices of the triangle will be perpendicular to the other sides.

Slope of BC  =  (y2 - y1)/(x2 - x1)

=  (5 + 5) / (4 + 4)

=  10/8

=  5/4

Slope of AD  =  -1/slope of BC

Slope of AD  =  -1 / (5/4)  =  -4/5

Slope of AC  =  (y2 - y1)/(x2 - x1)

=  (5 - 7) / (4 + 5)

=  -2/9

Slope of BE  =  -1/slope of AC

Slope of BE  =  -1 / (-2/9)  =  9/2

Slope of AB  =  (y2 - y1)/(x2 - x1)

=  (-5 - 7) / (-4 + 5)

=  -12/1

=  -12

Slope of CF  =  -1/slope of AB

Slope of CF  =  -1 /(-12)  =  1/12

After having gone through the stuff given above, we hope that the students would have understood, how to find the slope of median and altitude of a triangle.

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