I need help understanding these questions.?

Question

1. Point C is the midpoint of AB, D is the midpoint of AC , E is the midpoint of CB and F is the midpoint of DB . On a piece of paper, draw a diagram that represents this situation.

If CF=x, find the length of the following in terms of x:

a. DA

b. FB

2. On FL, how many points are there whose distance from L is 6cm?

Hint: Think about all the possibilities for the location of L.

3. B is between A and C. If AB = 6x, BC = x2, and AC = 27, find the value(s) of x. Be sure to show all work and verify your solutions.

4. Points P, Q, R, S, and T are all collinear. RP = PS, PQ = QR, and PS = ST.

T is not between R and S. If ST = 6, find the measurement of QT.

5. Points A and T divide MH into a ratio of 9:4:5 respectively. MH=108, and A is between M and T.

Draw a figure to represent the situation.

a. Find MA

b. Find AH

c. Which point is the midpoint of MH? Justify your answer

Thanks!

Answer 1

1.

a = 2x

b = 3x

2.

Where is L?  No mention of it in the problem statement.  So we assume its a new line.  There are only two points 6cm away from L in a straight line, but only one of them is between F and L.  The answer is therefore 1

3.

27 = 6x + 2x

27 = 8x

27/8 = 3.375 = x

4.

Answer 2

1.0   A___D___C_F_E___B

if CF = x, then DA=2x and FB = 3x

2.0 what is an FL?

3.0 A_____B________C (B is between but not in the midspan)

therefore: 6x + x² = 27

               x² + 6x - 27 =0

               (x + 9)(x - 3) = 0

               x = -9 ; x =3

4.0 R__Q__P____S____T

if ST = 6 then QT = QP + PS + ST ; PS = ST and QP = PS/2

QT = 6/2 + 6 + 6 = 15

5.0 M_________A____T_____H the problem says "divide into ratio RESPECTIVELY" so A is not between MT but MH.please check the problem

Answer 3

Few answers:

1. Imagine it like this:

A - - D - - C - F - E - - B

The trickiest part is just figuring out where F goes, but it should be somewhere between C and E.

a) 2x

b) 3x

2. I'm not too sure about this one. Do they give you a line?

3. 6x + 2x = 27

8x = 27

x= 27/8 or 3.375

4. Collinear means all the point lay on the same line.

R -- Q -- P -- S -- T

ST = 6, so therefore PS = 6. It is given that RP = PS, so RP is also 6.

Given PQ = QR; if you look at the line, PQ and QR are two segments that make up RP, right? So divide RP by half, 6/2 = 3. PQ = QR = 3.

QP + PS + ST

3 + 6 + 6 = 15.

QT = 15

5. Imagine the line like this:

M -- A -- T -- H

MA = 9x

AT = 4x

TH = 5x

To find the points, solve this equation, since you know the whole line, MH = 108.

9x + 4x+ 5x = 108

18x = 108

x = 6

a) MA = 9x = 9 * 6 = 54

b) AH = 4x + 5x = (4*6) + (5*6) = 24+30 = 54

c) A is the midpoint since MA and AH are the same lengths.

Answer 4

1) This woudl just be a straight line, draw one a do the following:

Lable the two endpoints A and B respectively

Find the midpoint between the two and label as C

Find the midpoint between A and C and label D

Find the midpoint between C and B and label E

You should now have a symetric set of 5 points on a line

The last one should be at the midpoint between D and B, which should be at the midpoint of C and E

To answer the question part of it, if CF is = to x, then DA would equal 2x and BF would equal 3x.  You have essentiall created a ruler and are measuring it off with marks, CF being the smalles division

2) Not sure where L came from but I'm assuming its another point on the line so there are 2 possible locatiions, could be 6 cm in either direction from F.  If this is not a line and a new problem then there are infinite possible locations 6 cm from F, think of a circle

3) Form an equation using what you know

AC =27 = AB + BC

27 = 6x + 2x

27 = 8x

x = 3.375

4) OK, looking at the info notice that RP = PS and PS = ST so RP, PS and ST are all the same values, which are all = to 6.  

To make the PQ=QR equation true it must be at the midpoint of those two points and looking at the other relationships Q and R must be between P and S.  PS = ST so split 6 into three parts , so its 2

The result figure I got was R, P, S, T along a line equal spaced, then QR in between P and S

5) So the figure would be a line again from L to right M A T and H you need to space them according to the ratios

MA is 1/2 the distance of MH ( it has ratio of 9 vs the other two parts of 4+5 =9, so 1/2 of the total 18 parts), so it is 54

AH = The compliment of this number to the total

AH = MH-MA = 108 - 54 = 54

The midpoint is Point A per the discussion above