TSO MATH EIS:Section Formula for Internal Division EIS คณิต กับ ครูโซ่ ยอดหทัย รีศรีคำ

TSO MATH EIS:Section Formula for Internal Division EIS คณิต กับ ครูโซ่ ยอดหทัย รีศรีคำ

Section Formula for Internal Division

Let us take a line with two end points A(x1, y1) and B(x2, y2). Consider a point P(x, y) which can divide the given line. Based on the presence of point P, we have two types of section formula.

Section formula for internal division:

If a point P, divides the line internally, we have the following formula.

Representation of section formula for internal division:

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  • น.ส. รัตนากร ใจสุข

    My name’s Miss.Rattanakorn Jaisook secondary 6/2 No.28

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 5:3 when A(x1, y1) = (-4, 2) and B(x2, y2) = (10, -4)
    Solution:
    Given: (x1, y1) = (-4, 2), (x2, y2) = (10, -4) m:n = 5:3

    x = (nx1+mx2)/(m+n) = (3(-4)+5(10))/(5+3)

    = (-12+50)/8

    = 38/8

    ∴x=4.75

    y = (ny1+my2)/(m+n) = (3(2)+5(-4))/(5+3)

    = (6-20)/(8 )

    = (-14)/8

    ∴y = -1.75

    Answer: P(x,y) = (4.75, -1.75)

  • https://www.facebook.com/juggy.mummy วราภรณ์ ดีรัตน์

    My name’s Miss. Waraphon Deerat Secondary 6/2 No.29

    My Question : Write the coordinate of the point P when it divides the line AB internally in the ratio of 9:6 where A(x1,y1) = (12,8) and (x2,y2) = (15,9)

    Solution
    Give : (x1,y1) = (12,8) (x2,y2) = (15,9) m:n = 9:6

    X = (mx2+nx1)/(m+n) = (9(15)+6(12))/(9+6)
    = (135+72)/15
    = 207/15
    = 13.8

    Y = (my2+ny1)/(m+n) = (9(8)+6(9))/(9+6)
    = (72+54)/15
    = 126/15
    = 8.4

    Answer P(x,y) = (13.8,8.4)

  • น.ส.ณัชญา สุวรรณโชติ

    My name’s natchaya suwannachote secondary 6/2 No.21
    Write the coordinate of the point P when it divides the line AB internally in the ratio of 2:11 when A(x1, y1) = (-8, 6) and B(x2, y2) = (15, -3)
    Solution:
    Given: (x1, y1) = (-8, 6) (x2, y2) = (15, -3) m:n = 2:11
    x = (mx1+nx2)/(m+n)
    = 11(-8)+2(15)/11+2
    = -88+30/13
    = -58/13
    x=-4.4
    y = (my1+ny2)/(m+n)
    = 11(6)+2(-3)/13
    = 66+(-6)/13
    = 60/13
    y = 4.6
    Answer: P(x,y) = (-4.4,4.6)

  • น.ส. จณิสตา อัมพรมหา ม.6/2 เลขที่ 17

    My name’s Miss.Janisata Umpornmaha secondary 6/2 No.17
    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:9 when A(x1, y1) = (-6, -3) and B(x2, y2) = (7, 2)
    Solution:
    Given: (x1, y1) = (-6, -3), (x2, y2) = (7, 2) m:n = 4:9
    X = (nx1+mx2)/(m+n)
    = (9(-6)+4(7))/(4+9)
    = (-54+28)/13
    = (-26)/13
    ∴x =4.75
    y = (ny1+my2)/(m+n)
    = (9(-3)+4(2))/(4+9)
    = (-27+8)/13
    = (-19)/13
    ∴y =-1.46
    Answer: P(x,y) = (4.75, -1.46)

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  • Kasidit sanong

    My name’s Miss.Rattanakorn Jaisook secondary 6/2 No.28

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:1 when A(x1, y1) = (5, -3) and B(x2, y2) = (-7, 4)
    Solution:
    Given: (x1, y1) = (5,-3), (x2, y2) = (-7, 4) m:n = 4:1

    x = (nx1+mx2)/(m+n) = (4(-7)+1(5))/(4+1)

    = (-28+5)/5

    = -23/5

    ∴x=-4.6

    y = (ny1+my2)/(m+n) = (4(4)+1(-3))/(4+1)

    = (16+(-3))/(5)

    = (13)/5

    ∴y = 2.6

    Answer: P(x,y) = (-4.6, 2.6)

  • นางสาวณัฐฐา อุดม

    My name’s Nuttha Udom Secondary 6/2 No.20
    Write the coordinate of the point B when it divides the line AB internally in the ratio of 3:2 when A(x1, y1) = (6, 2) and B(x2, y2) = (x, y)

    6 = 2 (6) + 3x / 3+2
    6 = 12 + 3x / 5
    30 = 12 + 3x
    18 = 3x
    6 = x

    8 = 2 (2) + 3y / 3+2
    8 = 4 + 3y / 5
    40 = 4 + 3y
    36 = 3y
    12 = y

    Answer: B(x,y) = (6, 12)

  • น.ส.ปนัดดา กิจสุวรรณ

    My name’s Miss.panadda kitsuwan secondary 6/2 No.38
    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:9 when A(x1, y1) = (-6, -3) and B(x2, y2) = (7, 2)
    Solution:
    Given: (x1, y1) = (-6, -3), (x2, y2) = (7, 2) m:n = 4:9
    X = (nx1+mx2)/(m+n)
    = (9(-6)+4(7))/(4+9)
    = (-54+28)/13
    = (-26)/13
    ∴x =4.75
    y = (ny1+my2)/(m+n)
    = (9(-3)+4(2))/(4+9)
    = (-27+8)/13
    = (-19)/13
    ∴y =-1.46
    Answer: P(x,y) = (4.75, -1.46)

  • น.ส.ปนัดดา กิจสุวรรณ

    My name’s panadda kitsuwan secondary 6/2 No.38
    Write the coordinate of the point P when it divides the line AB internally in the ratio of 2:11 when A(x1, y1) = (-8, 6) and B(x2, y2) = (15, -3)
    Solution:
    Given: (x1, y1) = (-8, 6) (x2, y2) = (15, -3) m:n = 2:11
    x = (mx1+nx2)/(m+n)
    = 11(-8)+2(15)/11+2
    = -88+30/13
    = -58/13
    x=-4.4
    y = (my1+ny2)/(m+n)
    = 11(6)+2(-3)/13
    = 66+(-6)/13
    = 60/13
    y = 4.6
    Answer: P(x,y) = (-4.4,4.6)

  • Buffering J’Jao

    My name’s Watcharapong Zaekor secondary 6/2
    No.10

    Write the coordinate of the point P when it
    divides the line AB internally in the ratio of 4:9 when A(x1, y1) = (5, 7) and
    B(x2, y2) = (4, 6)

    Solution:

    Given: (x1, y1) = (5,7), (x2, y2) = (4, 6) m:n =
    4:9

    X = (nx1+mx2)/(m+n)

    = (9(5)+3(4))/(3+6)

    = (45+12)/9

    = 57/9

    ∴x =6.33

    y = (ny1+my2)/(m+n)

    = (6(7)+3(6))/(3+6)

    = (42+18)/9

    = (60)/9

    ∴y =6.66

    Answer: P(x,y) = (6.33,6.66)

  • น.ส.อรพิณ อาจิณ

    My name’s Miss.Orapin Arjin secondary 6/2 No.31
    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:8 when A(x1, y1) = (-5,-4) and B(x2, y2) = (3,6)

    Solution: Given: (x1, y1) = (-5,-4), (x2, y2) = (3,6) m:n = 4:8

    X = (nx1+mx2)/(m+n)

    = (8(-5)+4(3))/(4+8)

    = (-40+12)/12

    = (-28)/12

    ∴x=2.3

    y = (ny1+my2)/(m+n)

    = (8(-4)+4(6))/12

    = (-32+24)/12

    = (-8)/12

    ∴y=-0.6

    Answer: P(x,y) = (2.3, -0.6)

  • D’Domy Anuwat

    My name’s Mr. Anuwat Meebun M. 6/2 No.14

    25. Write the coordinate of the point P when it divides the line AB internally
    in the ratio of 6:8 when A(x1, y1) = (-6,-4) and B(x2, y2) = (2,6)

    Solution: Given: (x1, y1) =
    (-6,-4), (x2, y2) = (2,6) m:n = 6:8

    X = (nx1+mx2)/(m+n)

    = (8(-6)+6(2))/(6+8)

    = (-48+12)/14

    = (-36)/14

    ∴x=2.52

    y = (ny1+my2)/(m+n)

    = (6(-4)+4(6))/14

    = (-32+36)/14

    = (4)/14

    ∴y=0.28

    Answer:
    P(x,y) = (2.52, 0.28)

  • น.ส. ดารณี สมคิด

    Miss Daranee Somkit M.6/2 No.22

    25. Write the coordinate of the point P when it divides the line
    AB internally in the ratio of 1:3 when A(x1, y1) = (-8, 2) and B(x2, y2) = (6,
    -6)

    Solution:

    Given: (x1, y1) = (-8, 2),
    (x2, y2) = (6, -6)
    m:n = 1:3

    x = (nx1+mx2)/(m+n)

    = (3(-8)+1(6))/(1+3)

    = (-24+6)/4

    = 18/4

    ∴x=4.5

    y = (ny1+my2)/(m+n)

    = (3(2)+1(-6))/(1+3)

    = (6-6)/(4)

    = (0)/4

    ∴y = 0

    Answer: P(x,y) = (4.5, 0)

  • น.ส. ดารณี สมคิด

    Miss Daranee Somkit M.6/2 No.22

    25. Write the coordinate of the point P when it divides the line
    AB internally in the ratio of 1:3 when A(x1, y1) = (-8, 2) and B(x2, y2) = (6,
    -6)

    Solution:

    Given: (x1, y1) = (-8, 2),

    (x2, y2) = (6, -6)

    m:n = 1:3

    x = (nx1+mx2)/(m+n)

    = (3(-8)+1(6))/(1+3)

    = (-24+6)/4

    = 18/4

    ∴x=4.5

    y = (ny1+my2)/(m+n)

    = (3(2)+1(-6))/(1+3)

    = (6-6)/(4)

    = (0)/4

    ∴y = 0

    Answer: P(x,y) = (4.5, 0)

  • Phasakorn Tongthumkit

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:8 when A(x1, y1) = (2,4) and B(x2, y2) = (4,)

    Solution: Given: (x1, y1) = (2,4), (x2, y2) = (4,3) m:n = 4:1

    X = (nx1+mx2)/(m+n)

    = (4(4)+1(2))/(4+1)

    = (16+2)/5

    = (18)/5

    ∴x=3.6

    y = (ny1+my2)/(m+n)

    = (4(3)+1(4))/5

    = (12+4)/5

    = (16)/5

    ∴y=3.2

    Answer: P(x,y) = (3.6, 3.2)

  • Montira ‘Xaou

    My name’s Miss.Montira
    Hiamhan secondary 6/2 No.27

    25. Write the co-ordinate of
    the point P when it divides the line AB internally in the ratio of 11:10 when
    A(x1, y1) = (-5, 3) and B(x2, y2) = (-2,1)

    Sol. Given:

    (x1, y1) = (-5, 3)

    (x2, y2) = (-2,1)

    m:n = 11:10

    x = (nx1+mx2)/(m+n)

    = (10(-5)+11(-2))/(11+10)

    = (-50-22)/21

    = -72/21

    ∴x= -3.42

    y = (ny1+my2)/(m+n)

    = (10(3)+11(1))/(11+10)

    = (30+11)/21

    = 41/21

    ∴y = 1.95

    Answer: P(x,y) = (-3.42 ,1.95)

  • นายนพรุจ คำเขียว

    นายนพรุจ คำเขียว 6/2
    Write the coordinate of the point P when it

    divides the line AB internally in the ratio of 4:9 when A(x1, y1) = (6, 8) and
    B(x2, y2) = (9, 5)

    Solution:

    Given: (x1, y1) = (6,8), (x2, y2) = (9, 5) m:n =
    4:9

    X = (nx1+mx2)/(m+n)

    = (9(6)+3(9))/(4+9)

    = (54+18)/13

    = 72/13

    ∴x =5.5

    y = (ny1+my2)/(m+n)

    = (9(8)+3(5))/(4+9)

    = (72+15)/13

    = (87)/13

    ∴y =7.6

    Answer: P(x,y) = (5.5,7.6)

  • เบญจรัตน์ มูลศรีแก้ว

    Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:10 when A(x1, y1) = (2,13) and B(x2, y2) = (5,20)

    X = nx1+my1/m+n
    = 10(2) + 4(13)/4+10
    = 20 + 42/14
    = 62/14
    = 4.42

    Y =nx2+my2/m+n
    = 10(5) + 4(20)/4+10
    = 50 + 80/14
    = 130/14
    = 9.28

  • น.ส.ปรียา กระโห้ทอง

    My name’s Miss.Namassikarn Suwanachote secondary 6/2 No.24

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 3:4 when A(x1, y1) = (2, 7) and B(x2, y2) = (5, 8)

    Solution: Given: (x1, y1) = (2, 7) (x2, y2) = (5, 8) m:n = 3:4

    X = nx1+mx2 / m+n
    = 4(2)+3(5) /3+4
    = 6+15 / 7
    = 21 / 7
    ∴x=3

    y = ny1+my2 / m+n
    = 4(7)+3(8) / 7
    = 28+24 / 7
    = 52 / 7
    ∴y = 7.42

    Answer: P(x,y) = (3, 7.42)

  • นายวินิจ มีบุญ

    My name’s Winit Meebun secondary 6/2 No.11

    Write the coordinate of the point P when it divides the line AB internally in the ratio of 2:3 when A(x1, y1) = (3, 5) and B(x2, y2) = (4, 6)

    Sol.
    x=2*3+1*4/2+3
    =6+4/5
    =10/2
    x=2

    y=2*5+3*6/2+3
    =10+18/5
    =28/5
    y=4.3

  • นลัทพร เกษารัตน์

    My name’s Miss.Nalattapron
    Kasarat secondary 6/2 No.25

    Write the coordinate of the point P when it divides the line
    AB internally in the ratio of 2:4 when A(x1, y1) = (10, 2) and B(x2, y2) = (8,4)

    Solution: Given: (x1, y1) = (10, 2) (x2, y2) = (8, 4) m:n =
    2:4

    X = nx1+mx2 / m+n

    = 4(10)+2(8) /2+4

    = 40+16 / 6

    = 46/ 6

    ∴x=7.66

    y = ny1+my2 / m+n

    = 4(2)+2(4) / 2+4

    = 8+8 / 6

    = 16/ 6

    ∴y = 2.66

    Answer: P(x,y) = (7.66,2.66)

  • ปรียา กะโห้ทอง

    My name’s preeya kahotong secondary 6/2 No.37

    Write the coordinate of the point P when it divides
    the line AB internally in the ratio of 2:10 when A(x1, y1) = (4, 5) and B(x2,
    y2) = (6, -7)

    Solution:

    Given: (x1, y1) = (4,5) (x2, y2) = (6, -7) m:n = 2:10

    x = (mx1+nx2)/(m+n)

    = 2(4)+10(6)/2+10

    = 8+60/12

    = 68/12

    x=5.6

    y = (my1+ny2)/(m+n)

    = 2(5)+10(-7)/12

    = 10+(-70)/12

    = -60/12

    y = -5

    Answer: P(x,y) = (5.6,-5)

  • นาย สุพิฌา วิทนาลัย

    My name’s Mr.Supicha Wittayalai secondary 6/2 No.12

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 6:3 when A(x1, y1) = (10, 1) and B(x2, y2)= (5, 2)

    Solution: Given: (x1, y1) = (10,1) (x2, y2) = (5, 2) m:n = 6:3

    X = nx1+mx2 / m+n
    = 3(10)+6(5) / 6+3
    = 30+30 / 9
    = 60 / 9
    ∴x=6.6

    y = ny1+my2 / m+n
    = 3(1)+6(2) / 9
    = 3+12 / 9
    = 15 / 9
    ∴y = 1.6

    Answer: P(x,y) = (6.6, 1.6)

  • นาย ภัทรวิทรย์ จริตซื่อ

    My name’s Mr.Phattarawit Jaritser secondary 6/2 No.8

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 4:7 when A(x1, y1) = (5, 2) and B(x2, y2) =(3, 10)

    Solution: Given: (x1, y1) = (5,2) (x2, y2) = (3, 10) m:n = 4:7

    X = nx1+mx2 / m+n
    = 7(5)+4(3)/ 4+7
    = 35+12 / 11
    = 47 / 11
    ∴x=4.27

    y = ny1+my2 / m+n
    = 7(2)+4(10) / 11
    =14+40 / 11
    = 54 / 11
    ∴y = 4.9

    Answer: P(x,y) = (4.27, 4.9)

  • น.ส.นมัสสิการ สุวรรณโชติ

    My name’s Miss.Namassikarn Suwanachote secondary 6/2 No.24

    25. Write the coordinate of the point P when it divides the line AB internally in the ratio of 3:4 when A(x1, y1) = (2, 7) and B(x2, y2) =(5, 8)

    Solution: Given: (x1, y1) = (2,7) (x2, y2) = (5, 8) m:n = 3:4

    X = nx1+mx2 / m+n
    = 7(5)+4(3)/ 3+4
    = 6+15 / 7
    = 21 / 7
    ∴x=3

    y = ny1+my2 / m+n
    = 4(7)+3(8) / 7
    = 28+24 / 7
    = 52 / 7
    ∴y = 7.42

    Answer: P(x,y) = (4.27, 4.9)