Question

prove: the segment joining the midpoints of the two sides of a triangle is parallel to the third side. the coordinates are A(0,0)B(a,0)on the the x axis, and C(c,d), M is midpoint and the coordinates of M is (c/2,d/2) and N is also a midpoint whose coordinates are (a+c/2, d/2) Please help fill in the blanks M=(0+____/2, 0+_____/2)=(_____/2, _____/2) and then N=(______+C/2, 0+________/2)=(______+C/2, _________/2)

slope of MN = d/2 _____d/2 = _______
____________ a+c/2-c/2 =________ a+c/2 - c/2

slope of AB = ______-______=_______=____
a a


please any help would be greatly appreciated thanks so much!!!!

Answer 1

For the x of the midpoint, add the x-coordinates of the two endpoint and divide by 2, (averaging them)

So for M we get
( (0+c)/2 , (0+d)/2) = (c/2, d/2)
for N
( (a+c)/2 , (d+0)/2) = ( (a+c/2 , d/2)

slope of MN = (d/2 - d/2)/((c+a)/2 - c/2)
= 0/ ??? = 0

slope of AB = (0-0)/(a-0) = 0/a = 0

so MN || AB