What is the equation of median of BC if A(2,2) and the equations of medians of AC and AB are 2x+y-2=0, x-y+2=0?
The median that is running from the vertex A is intercepting the other two medians. The intercepting point is the centroid of the triangle ABC.
To write the equation of the median, we need at least two points. Since we know the coordinates of the vertex A, we'll determine the coordinates of the centroid. For this reason, we'll solve the system of equations of the medians that are running from B and C vertices.
2x + y = 2 (1)
x - y = -2 (2)
We'll solve this system using eliminationmethod. We'll add (1)+(2):
3x = 0 => x = 0
0 - y = -2 => y = 2
Now, we'll write the equation of the median that is running from A and passes through the centroid whose coordinates are G(0,2):
(xG- xA)/(x - xA) = (yG-yA)/(y-yA)
(0-2)/(x-2) = (2-2)/(y - 2)
We'll cross multiply and we'll get:
0*(x-2) = -2*(y-2)
-2*(y-2) = 0
y - 2 = 0
y = 2
The requested equation of the median that is running from vertex A is y = 2.