Question

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

Answer:

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

Answer 2

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.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, 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.

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

Then we know

$\rm AM = MB \\\\NC = ND$

Then we have

$\begin{aligned} \rm AM + MB &= \rm AB\\\\ \rm AM+AM &=6 \\\\ \rm AM &= 3 \end{aligned}$

Similarly, we have

$\begin{aligned} \rm NC + ND &= \rm DC\\\\ \rm NC+NC &=6 \\\\ \rm NC &= 3 \end{aligned}$

NC = ND = 3 cm

AM = MB = 3 cm

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.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567