Geometry Honors 07-08 1st Semester

Wednesday, September 19, 2007

#4.3 Midpoint and Slope Conjectures

Aim 1: to find the midpoint between two coordinate points
Aim 2: to determine the slope of a line

  • (1-11) all
  • (12-18) even
  • (19)
  • (23-27) all
  • (29)
  • (31-32) all
  • (35-39) all

#4.4 Slopes of Parallel and Perpendicular Lines

Aim 1: to know and use the slopes of parallel lines to solve problems

Aim 2: to know and use the slopes of perpendicular lines to solve problems

  • (2-14) even
  • (15-16)
  • (18-19) all

You MUST post an answer AND explanation for credit!

Be sure to identify yourself by last name and which period you're in! Also, please label which section and problem # you are doing. For example, #4.4, #18:

There are 43 problems in all and 53 students between my 2 classes. For the ten of you who aren't able to post an answer, you will have make up your own problem and solution.

posted by msichan at 9/19/2007 12:34:00 PM

57 Comments:

  • 4.3 #1:
    line AB is negative, because the line leans towards the left, and when number on a number line go to the left, they're negative.
    line CD is zero, because if a line is vertical, it's slope is zero.
    line EF is positive, because it leans to the right, and when numbers on a number line go to the right, they're positive.
    finally, line GH is undefined, because if a line is horizontal, it is undefined. :)

    By Blogger aep3, At September 19, 2007 at 3:39 PM  

  • 4.3 #2

    the midpoint of the segments is (3,4)
    (12,-7) and (-6,15) are the coodernates. to find the midpoint, add both X's, add both Y's, and divide them both by 2.

    -nick stone p.3

    By Blogger NStone_ftw, At September 19, 2007 at 3:52 PM  

  • 4.3 #3

    Answer: -9, 3/2

    To find the coordinates of the midpoint of a segment joining two points, you must find the average of the Xs and the Ys of the two points. The two points are (-17,-8) and (-1,11). First, find the average of X1 and X2. X1 is -17 and X2 is -1. The average of the Xs is -9. Now you must find the average of the two Ys. The two Ys are -8 and 11. The average of the two Ys is 3/2 or 1.5

    - Cilia :)

    By Blogger C.Nazef, At September 19, 2007 at 4:12 PM  

  • Oh, Cilia- Period 3

    By Blogger C.Nazef, At September 19, 2007 at 4:13 PM  

  • midpoint of the segments (14,-7) and (-3,18). (x1,y1) and (x2,y2). You have to add x1 and x2 and then divide them by 2. 14+(-3) = 11. Since it will be 5.5 you just leave 11/2 as a fraction. then you do -7+18= 11.
    so the midpoint is. (11/2, 11/2)

    -adam shemony. per. 3

    By Blogger shemony, At September 19, 2007 at 4:17 PM  

  • oops the answer i did was #4 in case you were wondering. sorry

    By Blogger shemony, At September 19, 2007 at 4:21 PM  

  • This comment has been removed by the author.

    By Blogger dani.herrera.p.4, At September 19, 2007 at 4:41 PM  

  • This comment has been removed by the author.

    By Blogger *maria*, At September 19, 2007 at 4:48 PM  

  • #6 4.3

    Sketch a parallelogram. label the vertices A, B, C , and D. write the points down on the corresponding vertex A (0,0), etc. Draw the diagonals (A -> C and B -> D). Treat each diagonal as a line segment and find the average of the x and y's. You should get (6,4) for AC and BD.

    ---- Jared Period Four

    By Blogger JGH, At September 19, 2007 at 4:50 PM  

  • 4.3 #5
    For this you just reverse the operations you would have done to find the midpoint. Simply find the difference between (12,-8) which is the given endpoint and the midpoint (3,18).
    Once you have found the difference which turns out to be (-9,26).
    Now you have all the information you need to find the other endpoint.
    Ohh btw Mrs.Chan, this is Daniel-A
    =]

    By Blogger dani.herrera.p.4, At September 19, 2007 at 4:56 PM  

  • 4.3 #18
    calculate the slope of the segment.

    line segment MN is horizontal.

    which means it has a slope of 0.

    so 0 is the answer.

    -angela 4th period

    By Blogger a.ocampo, At September 19, 2007 at 5:09 PM  

  • 4.3 #14
    the slope 4 line segment EF is -4/1
    it falls down 4 points which makes it -4 and then goes right 1

    By Blogger fell in a well, At September 19, 2007 at 5:13 PM  

  • 4.3 # 19

    Calculate the slope of the vertical line segment OP.
    you will find that is undefined because it will be 6 over 0.

    Fung-On ,Period 3

    By Anonymous Anonymous, At September 19, 2007 at 5:24 PM  

  • 4.3 per four #7
    3 coordinants would be(6,8)(9,12) (12,16).To find this you redraw the graph,find the rise over run or the slope(m).Then you apply this to your graph by starting at point (3,9)and then you add the slope which is 3/4 so you move over 3 to the right and then 4 down.The point you stop at should be (6,8)which is one of the possible answers and then you repeat from that point.
    you can also got different point by starting from point (0,0) and instead of moving down 4 you go up 4 and instead of going to the right 3 you go the left 3. whick would give you points (-3,-4)(-6,-8)and(-9,-12)
    ~Lee Tom~

    By Blogger $k@t3rboi, At September 19, 2007 at 5:42 PM  

  • 4.3 #12

    Find the slope of line segment AB.
    A (4,4) B (10,7)

    First, find the differences between the two Ys: 7-4 = 3
    Then, find the differences between the two Xs: 10 -4 = 6

    Your slope is 3/6

    *Vanessa Pulgar
    *P:3

    By Blogger Unknown, At September 19, 2007 at 6:09 PM  

  • 4.3 #4
    Find the midpoint of
    (14,-7) and (-3,8)
    First, find the average of the Xs and the Ys.(adding the Xs then dividing by two. Same for the Ys.)
    The midpoints for these coordinates are (11/2, 11/2)

    -Christie G.-P.3

    By Blogger cgomez, At September 19, 2007 at 6:13 PM  

  • How do you get the answer/set up ::cough:: for question #8

    By Blogger Sean [: \], At September 19, 2007 at 6:41 PM  

  • 4.3 #31
    the first skater is going faster because his speed is 3/1 and the 2nd skater is 2/2
    sp skater 1 would be faster

    ~justin ladrido~
    period 3

    By Blogger Jladrido, At September 19, 2007 at 7:00 PM  

  • 4.3 #31
    the faster skater is the 1st one beause he is going 3/1 and the 2nd skater is 2/2
    therefore the 1st skater s going faster

    By Blogger Jladrido, At September 19, 2007 at 7:01 PM  

  • 4.3 # 10

    Solve for y; 3x+2y=12.

    To get the answer, you must move everything except the 2y to the opposite side. Then, you isolate y by dividing by 2. Then you can simplify the 12-3x over 2 by getting the answer 6-3x over 2.

    rcollin P4

    By Blogger R.Collin, At September 19, 2007 at 7:24 PM  

  • This comment has been removed by the author.

    By Blogger LaUrA.M, At September 19, 2007 at 7:43 PM  

  • This comment has been removed by the author.

    By Blogger Anonymous, At September 19, 2007 at 7:44 PM  

  • This comment has been removed by the author.

    By Blogger LaUrA.M, At September 19, 2007 at 7:47 PM  

  • hey its Josh Goldberg from period 3...Im doing 4.3 number 11.

    original problem is: 3y-18=2x
    the answer is Y=2/3x+6

    what you need to do is first move the 18 to the other side of the equal sign so you get 3y=2x+18

    Then you need to divide everything by 3 so you get y=2/3x+6.

    By Blogger JGOLDBERG, At September 19, 2007 at 7:47 PM  

  • period 4
    4.3 #15
    calculate slope for each segment Line GH

    point G(6,2) point H(8,5)

    (slope Formula)

    (rise)Y1-Y2
    ------------- =
    (run)X1-X2
    so...Y1=2 ,Y2=5 ,X1=6 ,X2=8

    2-5
    ---- =
    6-8
    Witch =to

    -3
    ---
    -2

    By Blogger LaUrA.M, At September 19, 2007 at 7:58 PM  

  • 4.3 #2
    to find the midpoint of (12,-7) and (-1,11) you first find the average of the x's then the y's and thats midpoint
    answer- (3,4)

    By Blogger romina.4, At September 19, 2007 at 8:04 PM  

  • 4.3#9

    Answer: Yes it does matter if u subtract the x's and y's in order, Also, x has to be listed first. for an example:
    (2,1), (1,2)= 1-2=-2
    over 2-1=1
    the answer would be m=-2 over 1. It wouldn't end out to be the same if thery weren't in order.

    By Blogger Anonymous, At September 19, 2007 at 8:11 PM  

  • Acosta, Per. 4
    4.3 #9
    Yes the order in which you subtract coordinates matters, because coordinates go (x,y) not (y,x). So you must subtract the x coordinates first then the y coordinates.

    By Blogger Tennis_Player_Pedro, At September 19, 2007 at 8:30 PM  

  • ♫4.3♫ # OCH☺(8)

    Well, the question states that pt. A is @ the ►origin(pt.0,0)◄ and pt. B is @ pt(9,6).

    yes?

    ♦so, to find the two trisection points, divide the X and Y of pt.B by 3, giving you (3,2).

    ☻next, what i did was used the slope method of rise over run.

    ♪Crescendo from pt.A, giving you (3,2). From there, do the same, giving you (6,4)

    ╬In Summation, your Points should be: A(0,0)...1st trisection(3,2)...2nd trisection(6,4)... and B(9,6)


    yeah.. i'm sure there's an easier way than making a graph, but for visual learners like myself, this seemed pretty elementary.. lessee if i get this right ☺..



    ♫~Cristina Casellas~♫
    ♪~Period 3~♪

    By Blogger CriFalconSoundzGr8, At September 19, 2007 at 8:33 PM  

  • My mistake, for 4.3#9- the example I made would be instead of 1-2=-2 it would be 1-2=-1.

    By Blogger Anonymous, At September 19, 2007 at 8:36 PM  

  • 4.3 #12
    calculate the slope of each segment.

    Point A lies on (4,4)
    Point B lies on (10,7)

    y1-y2
    -----
    x1-x2

    7-4
    ----
    10-4


    3/6 reduced= 1/2




    maria ibanez per-4

    By Blogger *maria*, At September 19, 2007 at 8:37 PM  

  • 4.3 #1


    line GH is undefined, because all horizontal lines have no slope.

    line EF is positive because the slant of the line leans towards the right, as you go to the right on a number line you still have positive numbers.

    line CD is 0 because it is vertial the slope is zero [ there is no slant ]

    the slope of line AB is negative because the slant goes to the left, which means the numbers are negative on the left of the number line.



    chaunte ladrido [ 4th hour ]

    By Blogger ladrido.c.4, At September 19, 2007 at 9:12 PM  

  • PEr 4
    im so smart!
    ok again
    4.3 #16

    calculate slope for each segment Line IJ



    (slope Formula)

    (rise)Y1-Y2
    ------------- =
    (run)X1-X2
    so...Y1=o ,Y2=-5 ,X1=0 ,X2=-6

    0-5
    ---- =
    o-6
    Witch =to

    -5
    ---
    -6

    By Blogger LaUrA.M, At September 19, 2007 at 9:38 PM  

  • 4.4 #1

    <--> <-->
    AB and BC
    A(1,2)
    B(3,4)
    C(5,2)
    The pair of lines will be perpendicular because ab and bc share the same point and the two lines will connect. When connected it'll form a X shape and all the angles are congruent

    Brian Chang
    Period 3

    By Blogger BrianC., At September 19, 2007 at 10:04 PM  

  • wait i got it wrong..

    actualy Y1=4,Y2=0,X=-6,X2=0

    Sooo
    Slope formula

    4-0
    ----=
    -6-0

    witch = to
    4/-6 simplifide to 2/-3

    that the correct answer!

    By Blogger LaUrA.M, At September 19, 2007 at 10:14 PM  

  • This comment has been removed by the author.

    By Blogger Big Mike~DT, At September 19, 2007 at 10:23 PM  

  • 4.3 #31

    Skater 1 has a slope of 3/2 and skater 2 has a slope of 2/2. So skater 1 is going faster by 1x because he has the bigger slope.

    Big Mike ~ DT #80
    ~*Period 3*~
    (The SMARTER Class)

    By Blogger Big Mike~DT, At September 19, 2007 at 10:29 PM  

  • my bad i meant #32 on my problem

    By Blogger Big Mike~DT, At September 19, 2007 at 10:31 PM  

  • 4.4 #2

    you have to determine whether line AB and line CD is a pair of parallel lines, perpendicular lines, or neither.


    #2 )
    first you find the slope of the 2 lines by
    Y1-Y2 over X1-X2


    A (1,2)
    B (3,4)

    calculate with formula
    2-4 / 1-3 =
    -2 / -2 =
    1

    so line AB slope = 1

    next find line CD slope.
    C (5,2)
    D (8,3)

    use formula
    2-3 / 5-8 =
    -1 / -3 =
    1/3

    so line CD slope = 1/3

    parallel lines have the same slope.
    CD slope = 1/3
    AB slope = 1
    not equal slopes, not parallel

    perpendicular lines have opposite reciprocal slopes.
    1/3 and 1 arent oppostie reciprocal so they arent perpendicular.

    this determines that lines AB and CD are NEITHER.

    samantha axelrod (:
    pd.4

    By Blogger sam.axelrod, At September 19, 2007 at 10:41 PM  

  • 4.3 #21 :

    Calculate the slope of line segment ST

    You can use the formula :
    to find the slope of these coordinate points
    S (9, -3)
    T (10, -2)

    y2- y1
    ------ -2 -(-3)
    x2 - x1 --------
    10 - 9

    The slope is 1/1 equivalent to 1
    It rises one unit and runs one unit


    :) Sabrina Stern
    P.4

    By Blogger sabby-stern, At September 19, 2007 at 10:54 PM  

  • 4.4 #15:

    the slope of H and A is 4/3, and N and D is 13.

    workings: -1-7/-5-1=
    8/6=
    4/3
    7+6/6-5=
    13
    the quadrilateral is a rectangle because it the vertices have the same angle measurement.
    the midpoint is (1/2,0) and (0,6). workings:
    -5+7/2, -1+1/2

    By Blogger rodriguez, At September 19, 2007 at 11:20 PM  

  • period 3. rodriguez.

    By Blogger rodriguez, At September 19, 2007 at 11:21 PM  

  • This comment has been removed by the author.

    By Blogger sabby-stern, At September 19, 2007 at 11:37 PM  

  • This comment has been removed by the author.

    By Blogger sabby-stern, At September 19, 2007 at 11:50 PM  

  • This comment has been removed by the author.

    By Blogger sabby-stern, At September 19, 2007 at 11:52 PM  

  • 4.3

    (#12)



    Find the slope of line segment AB
    A(4,4)
    B(10,7)

    (do rise over run)
    You have to find the
    differecnces b/t the two
    Y's
    7-4 = 3

    find the differences b/t the
    X's
    10 -4 = 6

    so the slope of line segment
    AB is 3/6

    SoLaNa peR: 3
    =D

    By Blogger SoLaNuHH, At September 20, 2007 at 12:46 AM  

  • Cera Gomez period 4

    #23
    To find the slope of (16,0) and (12,8) is to Minus 8 minus 0 then 12 minus 16. That makes it 8/-4 and you can reduce that to -2.

    By Blogger Cera, At September 20, 2007 at 5:40 AM  

  • molly spencer period 4
    4.3 #13
    i decided to use Y1-Y2 over X1-X2

    i got (13,11)(14,7)

    so it would be 11-7 over 13-14
    and that equals 4 over -1

    By Blogger Molly.S., At September 20, 2007 at 6:56 AM  

  • I am doing this now because when I got home from my game your web site wasn't working. Since there is 48 comments and only 43 problems I am making my own problem.

    Find the slope of (5,2) (6,9)

    To find the slope you have to do rise (Y) over run (X) you do
    (y1-y2) over (x1-x2).
    So (2-9) / (5/6) is -7/-1 which = 7

    M=7

    By Blogger Mkaladi, At September 20, 2007 at 8:17 AM  

  • im going to do 4.3 #14

    To find the slope of the line segment EF.... you do rise over run.
    The line segment goes 4 down and 1 over.
    so therefore the slope is -4/1.

    JUAN RAAD. Per 3

    By Blogger Unknown, At September 20, 2007 at 8:39 AM  

  • I did a question that was not assigned by mistake
    Is that ok?

    By Blogger sabby-stern, At September 20, 2007 at 9:25 AM  

  • mine is "made up"

    By Blogger sabby-stern, At September 20, 2007 at 9:36 AM  

  • i dont get problem ###6 in 4.3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    help please!!!

    By Blogger inukid, At September 20, 2007 at 12:34 PM  

  • Kayla Saunders p 4

    #23
    use the slope formula to dfind the midpoint of # 23.

    By Blogger kayla's a veg head., At September 20, 2007 at 12:35 PM  

  • Lohn 4th period.

    Because the website was not working and i could not figure out how to post the comment so i'm doing my own problem.

    Find the slope of (7,4) and (8/6)

    use the equation rise over run so you do (y2 - y1)/(x2 - x1.
    So (6-4)/(8-7)= 2/1 which is 2.

    By Blogger Unknown, At September 20, 2007 at 6:48 PM  

  • I need help with number #8 in 4.3

    By Blogger TNguyen, At September 20, 2007 at 9:09 PM  

  • Jessica Barquero
    Period # 3
    #10.4

    Answer: It's an ordinary quadrilateral

    Explanation: It is an ordinary quadrilateral because no two slopes are the same. ;]

    By Blogger Jessica, At September 20, 2007 at 11:33 PM  

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