# HOW TO FIND THE SLOPE OF A MEDIAN OF A TRIANGLE

## About "How to find the slope of a median of a triangle"

How to find the slope of a median of a triangle :

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

A line is passing through the midpoints of each side of triangle is known as median.

Let us look into some example problems to understand how to find median of triangle.

Example 1 :

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

Solution :

Let A (6 , 7),  B(2 , -9) and C(-4 , 1) be the vertices of triangle.

Midpoint of the side BC  =  D

Midpoint of the side AC  =  E

Midpoint of the side AB  =  F

Medians of triangle :

In order to find the slopes of the line AD, first we have to find the point D.

Midpoint  =  (x1 + x2)/2 ,  (y1 + y2)/2

Midpoint of the side BC  =  (2 + (-4))/2 , (-9 + 1)/2

=  (-2/2, -8/2)

= D (-1 , -4)

By using the points A and D, we may find the slope of the median AD.

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

Slope of median AD  =  (y2 - y1)/(x2-x1)

=  (-4 - 7)/(-1-6)

=  -11/(-7)

=  11/7

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

Midpoint of the side AC  =  (6 + (-4))/2 , (7 + 1)/2

=  (2/2, 8/2)

= E (1 , 4)

By using the points B and E, we may find the slope of the median BE.

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

Slope of median BE  =  (y2 - y1)/(x2-x1)

=  (4 - (-9))/(1 - 2)

=  (4 + 9)/(-1)

=  13/(-1)

=  -13

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

Midpoint of the side AC  =  (6 + 2)/2 , (7 + (-9))/2

=  (8/2, -2/2)

= F (4 , -1)

By using the points C and F, we may find the slope of the median CF.

C(1, 4) and F(4, -1)

Slope of median CF  =  (y2 - y1)/(x2-x1)

=  (-1 - 4)/(4 - 1)

=  -5/3

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