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

Answer 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.

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