Worksheet on Division of Line-Segment

In the worksheet on division of line-segment student’s need to find the co-ordinates of the point dividing the line segment joining two given points in a given ratio.

Let us recall the formula for finding the co-ordinates of the point dividing the line segment joining two given points in a given ratio as follows; 

Let P (x₁, y₁) and Q (x₂, y₂) be two given points. 

(a) If the point R divides the line-segment PQ internally in the ratio m : n, then the co-ordinates of R are {(mx₂ + nx₁)/(m + n) , (my₂ + ny₁)/(m + n)}. 

(b) If the point R divides the line-segment PQ externally in the ratio m : n, then the co-ordinates of R are {(mx₂ - nx₁)/(m - n), (my₂ - ny₁)/(m - n)}.

To learn more about the formula for finding division of line-segment Click Here.


1. (i) If A and B be the points (1, 5) and (- 4, 7), then find the point P which divides AB internally in the ratio 2 : 3. 

(ii) Find the co-ordinates of the point which divides the line-segment joining the points (2, - 5) and (- 3, - 2) externally in the ratio 4 : 3. 

(iii) Find the co-ordinates of the point which divides the line-segment joining the, points ( x + y, x - y) and (x - y, x + y) internally in the ratio x : y. 

(iv) Find the co-ordinates of the point which divides the line-segment joining the points (a, b) and (b, a) externally in the ratio (a - b) : (a + b). 


2. (i) Find the ratio in which the point (1, 2) divides the line-segment joining the points (- 3, 8) and (7, - 7).

(ii) Find the ratio in which the point (5, - 20) divides the line-segment joining the points (4, 7) and (1, - 2).


3. In what ratio the segment joining the points (3, 4) and (2, - 3) is divided by the x-axis ? Also find the ratio in which it is divided by the y-axis.


4. (i) P is a point on the line-segment AB such that AP = 3 PB ; if the co-ordinates of A and B are (3, -4) and (- 5, 2) respectively, find the 1 co-ordinates of P.

(ii) The line-segment CD is produced to Q such that 2 CQ = 5 DQ; if the co-ordinates of C and D are (4, 7) and (- 2, 4) respectively, find the co-ordinates of Q.

(iii) If the point (6, 3) divides the segment of the line from P (4, 5) to Q (x, y) in the ratio 2 : 5, find the co-ordinates (x, y) of Q. What are the co-ordinates of the mid-point of PQ?


5. If the point (0, 4) divides the line-segment joining the points (- 4, 10) and (2, 1) internally in a definite ratio, find the co-ordinate of the point which divides the segment externally in the same ratio.


6. The straight line joining the points (2, - 2) and (4, 6) is extended each way a distance equal to half its own length. Determine the co-ordinates of the terminal points.


7. Find the co-ordinates of the point of trisection of the line-segment joining the points (- 2, 3) and (3, - 1) that is nearer to (- 2, 3).


8. Show that the line-segment joining the points (8, 3), (- 2, 7) and the line-segment joining (11, - 2), (5, 12) are bisected each other.


9. Find the lengths of the medians of the triangle whose vertices are (2, - 4), (6, 2) and (- 4, 2).

10. If (4, 3), (-2, 7) and ( 0, 11) are the co-ordinates of the mid-points of the Indy, of a triangle, find the co-ordinates of its vertices. 

11. (i) Find (x, y) if (3, 2), (6, 3), (x, y) and (6, 5) are the vertices of a parallelogram taken in order. 

(ii) If (x₁, y₁), (x₂, y₂), (x₃, y₃) and (x₄, y₄) be the consecutive vertices of dparallelogram, show that, x₁ + x₃ = x₂ + x₄ and y₁ + y₃ = y₂ + y₄. 

Answers for the worksheet on division of line-segment are given below to check the exact answers of the above questions.

Answers:

1. (i) (-1, 29/5)

(ii) (- 18, 7)

(iii)((x² + y²)/(x + y) ,(x² - y² + 2xy)/(x + y))

(iv) ((a² + b²)/2b, (b² - a² + 2ab)/2b).


2. (i) Internally in the ratio 2 : 3.

(ii) Externally in the ratio 3 : 2


3. Internally in the ratio 2 : 3. and externally in the ratio 3 : 2


4. (i) (-3, 1/2)

(ii) (-6 , 2)

(iii) Q (x, y) ≡ (11 – 2) , Mid – Point : (15/2, 3/2 )


5. (8, -8)


6. (5, 10) and (1, -6)


7. (-1/3 ,5/3)


9. √89, √17 and 5√2 units.


10. (6 , 7) , (2, -1) , (-6, 15)


11. (i) (x , y) = (9, 6)


Co-ordinate Geometry

  • What is Co-ordinate Geometry?
  • Rectangular Cartesian Co-ordinates
  • Polar Co-ordinates
  • Relation between Cartesian and Polar Co-Ordinates
  • Distance between Two given Points
  • Distance between Two Points in Polar Co-ordinates
  • Division of Line Segment: Internal & External
  • Area of the Triangle Formed by Three co-ordinate Points
  • Condition of Collinearity of Three Points
  • Medians of a Triangle are Concurrent
  • Apollonius' Theorem
  • Quadrilateral form a Parallelogram
  • Problems on Distance Between Two Points
  • Area of a Triangle Given 3 Points
  • Worksheet on Quadrants
  • Worksheet on Rectangular – Polar Conversion
  • Worksheet on Line-Segment Joining the Points
  • Worksheet on Distance Between Two Points
  • Worksheet on Distance Between the Polar Co-ordinates
  • Worksheet on Finding Mid-Point
  • Worksheet on Division of Line-Segment
  • Worksheet on Centroid of a Triangle
  • Worksheet on Area of Co-ordinate Triangle
  • Worksheet on Collinear Triangle
  • Worksheet on Area of Polygon
  • Worksheet on Cartesian Triangle





  • 11 and 12 Grade Math 

    From Worksheet on Division of Line-Segment to HOME PAGE


    New! Comments

    Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



    Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



    Share this page: What’s this?

    Recent Articles

    1. Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition

      Mar 18, 24 02:31 PM

      Adding 5-digit Numbers with Regrouping
      We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We…

      Read More

    2. Adding 4-digit Numbers with Regrouping | 4-digit Addition |Addition

      Mar 18, 24 12:19 PM

      Adding 4-digit Numbers with Regrouping
      We will learn adding 4-digit numbers with regrouping. Addition of 4-digit numbers can be done in the same way as we do addition of smaller numbers. We first arrange the numbers one below the other in…

      Read More

    3. Worksheet on Adding 4-digit Numbers without Regrouping | Answers |Math

      Mar 16, 24 05:02 PM

      Missing Digits in Addition
      In worksheet on adding 4-digit numbers without regrouping we will solve the addition of 4-digit numbers without regrouping or without carrying, 4-digit vertical addition, arrange in columns and add an…

      Read More

    4. Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition

      Mar 15, 24 04:52 PM

      Adding 4-digit Numbers without Regrouping
      We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following exa…

      Read More

    5. Addition of Three 3-Digit Numbers | With and With out Regrouping |Math

      Mar 15, 24 04:33 PM

      Addition of Three 3-Digit Numbers Without Regrouping
      Without regrouping: Adding three 3-digit numbers is same as adding two 3-digit numbers.

      Read More