1) A median is the line that connects a vertex (point A in this case) with the midpoint of the opposite side, line segment BC. First the use the midpoint formula to find the midpoint (M) between B and C:
M = ((2+6)/2, (3+1)/2) = (4,2)
The median then is the line that passes through the points A=(1,-4) and M=(4,2). The line has the general formula y=mx + b where m is the slope and b is the y-intercept. First, use the slope formula to find the slope:
m = (2-(-4))/(4-1) = 2
So we have y = 2x + b. To find b, plug in the values of point A or M. I'll use point A:
y = 2x + b
2 = 2*4 + b
2 = 8 + b
-6 = b
So the equation of the line is:
y = 2x - 6
2) To find d, plug the point (d,3) into the equation of the line and solve for d:
y = 3x + 1
3 = 3d + 1
2 = 3d
2/3 = d
3) Same process as problem 2:
y = 3x + 2
5 = 3k + 2
3 = 3k
1 = k
