**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 :

AD, BE and CF

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

Midpoint = (x_{1} + x_{2})/2 , (y_{1} + y_{2})/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 = (y_{2} - y_{1})/(x_{2}-x_{1})

= (-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 = (y_{2} - y_{1})/(x_{2}-x_{1})

= (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 = (y_{2} - y_{1})/(x_{2}-x_{1})

= (-1 - 4)/(4 - 1)

= -5/3

- How to prove if the given points are collinear using slope
- Conditions for collinearity
- Conditions for collinearity of three points

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