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

Step-by-step explanation:

If M is the midpoint of AB, then AM = MB

Also AM+MB = AB

MB+MB = AB

2MB = AB

2MB = 6

MB = 6/2

MB = 3 cm

Also

If M is the midpoint of CD, then CN = DN and CN+DN = CD

CN+CN= CD

2CN = CD

2CN = 6

CN = 6/2

CN = 3 cm

Note that MN = MB + BC + CN

Substitute the given data

MN = 3cm + 6cm+3cm

MN = 12cm

Therefore the distance between M and N is 12cm

step-by-step explanation: