# A triangle has vertices at A(-3, 2), B(-5, -6), and C(5, 0). Determine the equation of the median from vertex A how do you find the median of a triangle?

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### 2 Answers

The median from a point in a triangle is the line drawn from one vertex to the mid point of the opposite side.

Here the vertexes of the triangle are given as A(-3, 2), B(-5, -6), and C(5, 0).

If we are to draw the vertex from point A, we need to do the following:

- Find the midpoint of BC

The midpoint is [(-5 +5 )/2 , (0-6)/2 ] or (0, -3).

- Draw the line from the point to the midpoint

The equation of the line from (-3,2) to (0,-3) is

y+3 = [(2+3)/ (-3-0)]* (x -0)

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

=>3y + 9 = -5x

=>5x + 3y +9 =0

**The required equation is 5x + 3y +9 =0**

The vertices of the triangle are A(-3, 2), B(-5, -6), and C(5, 0).

To find the median from A, to the other side BC, we have to find the mid point M of BC and then find the equation of the line through A and M.

M(x , y) = ( (xB+xC)/2 , (yB+yC)/2)

xM = (-5+5)/2 = 0

xM = (-6 +0)/2 = -3.

M(x ,y) =(0,-3)

Now we find the equation of the median AM, with A(-3,2) and M(0,-3).

We know that the line joining the points (x1 , y1) and (x2,y2) is:

y-y1 = {(y2-y1(/(x2-x1)}(x-x1).

Therefore the equation of AM is:-

y- -2) = {(-3-2)/(0 - 3)}(x- -3)

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

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

3y+6 =5x+10

5x-3y+10-6 =0

5x-3y+4 = 0

Therefore the equation of the median is 5x-3y+4 = 0 is the equation of the median through the vertex A of the triangle.