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!!!!
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
To fill in the blanks, we can substitute the given coordinates into the formulas for finding the midpoints:
For M:
M = ((0 + c) / 2, (0 + d) / 2) = (c / 2, d / 2)
For N:
N = ((a + c) / 2, (0 + d) / 2) = (a / 2 + c / 2, d / 2)
Now, let's calculate the slope of MN:
slope of MN = (d / 2 - d / 2) / (a / 2 + c / 2 - c / 2)
= 0 / (a / 2)
= 0
Next, let's calculate the slope of AB:
slope of AB = (0 - 0) / (a - 0)
= 0 / a
= 0
Since the slope of MN is 0 and the slope of AB is 0, we can conclude that MN is indeed parallel to AB.
To prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side, we can use the concept of slope.
Let's calculate the coordinates of M and N first:
M = (0 + c/2, 0 + d/2) = (c/2, d/2)
N = (a + c/2, 0 + d/2) = (a + c/2, d/2)
Now, let's calculate the slope of MN.
slope of MN = (change in y-coordinates)/(change in x-coordinates)
= (d/2 - d/2)/(c/2 - c/2) = 0/0
We get 0/0, which is an indeterminate form. This means that the slope of MN is undefined or parallel to the y-axis.
Now, let's calculate the slope of AB.
slope of AB = (change in y-coordinates)/(change in x-coordinates)
= (0 - 0)/(a - 0) = 0/a = 0
Since the slope of AB is 0, it is parallel to the x-axis.
Thus, we can conclude that the segment joining the midpoints of two sides of a triangle (MN) is parallel to the third side (AB).