If the coordinates of the vertices of the triangle ABC be A(-1,6), B(-3,-9), and C(5,-8) respectively. i) Find the coordinated of the midpoint of AB II) Find the equation of the median through C in the form ax+by+c=0

i) To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we use the formula ((x1+x2)/2, (y1+y2)/2).

For AB with A(-1,6) and B(-3,-9), the midpoint M would be:

M = ((-1-3)/2, (6-9)/2) = (-2, -1.5)

ii) The equation of a line in the form ax+by+c=0 can be found using the slope and a point on the line. The slope of a line through points (x1, y1) and (x2, y2) is (y2-y1)/(x2-x1).

The slope of the line through C(5,-8) and M(-2,-1.5) is:

m = (-1.5 - (-8))/(-2 - 5) = 6.5/-7 = -0.92857

The equation of the line is then y - y1 = m(x - x1), which simplifies to y = mx - mx1 + y1. Substituting the values we have:

y = -0.92857x - (-0.92857*-2) - 1.5 y = -0.92857x + 1.85714 - 1.5 y = -0.92857x + 0.35714

To put this in the form ax+by+c=0, we rearrange to get:

0.92857x + y - 0.35714 = 0

So the equation of the median through C is approximately 0.92857x + y - 0.35714 = 0.