Determine the length of median AD of triangle ABC with vertices A(-2,-1) , B(2,0), C(0,6).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

For the triangle ABC with vertices A(-2,-1) , B(2,0), C(0,6), the mid point of the side BC is ((2 + 0)/2 , (6 + 0)/2) or (1 , 3)

The distance of the median AD is the distance from the point A(-2 , -1) to (1, 3)

This is equal to sqrt[(-2 - 1)^2 + (-1 - 3)^2]

=> sqrt [ 9 + 16]

=> sqrt 25

=> 5

The length of the median AD is 5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The median AD joins the vertex A with the middle of the side BC.

Therefore, D is the middle of BC.

We'll calculate the coordinates of the midpoint D:

xD = (xB + xC)/2

xD = (2+0)/2

xD = 1

yD = (yB + yC)/2

yD = (0+6)/2

yD = 3

Now, we'll determine the length of AD;

[AD] = sqrt[(xD - xA)^2 + (yD - yA)^2]

[AD] = sqrt[(1 + 2)^2 + (3 + 1)^2]

[AD] = sqrt(9 + 16)

[AD] = sqrt25

[AD] = 5

The length of the median AD is: [AD] = 5 units.

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