The coordinates of the vertices of a scalene triangle are A (0, 0), B (2, 2), and          C (6, –6). What is the equation of the median from vertex A?  1 pointA. x – 2y = 0B. 2x – y = 0C. x + 2y = 0D. 2x + y = 0

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

First, we need to find the midpoint of the line segment BC. The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

Substituting the coordinates of points B(2,2) and C(6,-6) into the formula, we get:

Midpoint D = ((2+6)/2 , (2-6)/2) = (4, -2)

Now, we have the coordinates of point A (0,0) and the midpoint D (4,-2). We can find the equation of the line AD using the formula y = mx + c, where m is the slope and c is the y-intercept.

The slope m of a line through two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1).

So, m = (-2-0)/(4-0) = -1/2

Substituting m = -1/2 and the coordinates of point A into the equation y = mx + c, we get 0 = -1/2*0 + c. So, c = 0.

Therefore, the equation of the median from vertex A is y = -1/2x + 0, or 2y = -x.

Rearranging, we get x + 2y = 0, which corresponds to option C.