Question

HELP! A triangle has vertices X(0,0), Y(4,4) and Z(8,-4).
Write an equation for each of the 3 medians.

Answer 1

Start the question with drawing the triangle

Think about the definition of median, a median is the line from a vertice to the middle of the front side. so think about finding the middle of the sides. YX = Y-X = (4,4), middle of the YX/2= (4/2,4/2)= (2,2). using the same approach middle of ZX/2 = (4,-2) as well as ZY/2= (2,-4). Now the equation of each median can be found like finding the equation of any other line, using 2 points of it. one point is the middle of the side and the other point is the front vertice.
equation of the line: y-y0 = m (x-x0) where m is the slope (y2-y1/x2-x1)
for one median we have the YZ side that has it's middle point at (2,-4) and it's front vertice to be X=(0,0). Therefore it's slope is (-4-0)/(2-0)=-2.
so we have y+4=-2(x-2) and simplifying a bit we get ==> y = -2x
same manner we get: y=-x+4 and x = 4

Hope it's helpful

Answer 2

so would getting the median be m= y2 - y2 / x2 - x1?