Question

Hello! Please fill in all the blanks:

The points A, B, C, and D are plotted on a line, consecutively. AB = BC = CD = 6 cm. Find the distance between M and N, which are the midpoints of segments
AB

and

CD

, respectively. Fill in the blanks of the Statement/Reason solution.

Statement Reason

1. AM = BM = AB 2 =_____ cm 1. ____________________

2. CN = _____ = CD 2 = _____ cm 2. Def. of midpoint

3. MN = MB + ______ + CN 3. ____________________

4. MN = ________ cm 4. Algebra

1. The distance between of the AM = BM = AB/2  is 3 cm, NC = ND = DC is 3 cm, MN = MB + DC + NC, and MN is 6.
1. AM = BM = AB/2 = 3 cm.
2. NC = ND = DC = 3 cm.
3. MN = MB + DC + NC.
4. MN = MB + DC + NC = 3 + 6 + 3 = 12 cm.
Step-by-step explanation:
Using coordinate geometry, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Then we know
AM=MB
NC=ND
Then we have
AM+MB=AB
AM+AM=6
Similarly, we have
NC = ND = 3 cm
AM = MB = 3 cm