# Find the equation of median from the vertex A of triangle ABC if A(1,2), B(2,3), C(2,-5).

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We have to find the median from the vertex A of the triangle ABC.

Now, the mid point between B and C can be derived using the relation for the finding the mid point between two points. It states that the mid point between ( x1, y1) and (x2 , y2) is given by ( ( x1 + x2)/2, ( y1+ y2)/2).

The mid point between B(2,3) and C(2, -5) is (( 2+2)/2 , ( 3 - 5)/2)

=> ( 2 , -1)

The equation of the line joining A(1,2) and ( 2 , -1) is y+1=[(2+1)/(1-2)]*(x - 2)

=> y + 1 = -3*(x - 2)

=> y + 1 = -3x + 6

=> 3x + y - 5 = 0

**The required equation of the median is 3x + y - 5 = 0**

The median is joining the vertex and the middle of the opposite side. If the median starts from the vertex A, then, we'll have to determine the midpoint of the opposite side BC.

xM = (xB + xC)/2

xM = (2+2)/2

xM = 2

yM = (yB + yC)/2

yM = (3 - 5)/2

yM = -1

The coordinates of the midpoint M are: M(2 , -1).

Now, we'll write the equation of the median that passes through the points A and M.

(xM - xA)/(x - xA) = (yM - yA)/(y - yA)

(2 - 1)/(x - 1) = (-1- 2)/(y - 2)

1/(x - 1) = -3/(y - 2)

-3(x - 1) = y - 2

We'll remove the bracktes:

-3x + 3 + 2 = y

We'll use symmetric property and we'll combine like terms:

y = -3x + 5

**The equation of the requestedÂ median is: 3x + y - 5 = 0.**