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.
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
11 and 12 Grade Math
From Worksheet on Division of Line-Segment to HOME PAGE
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.
Dec 10, 24 02:35 PM
Dec 09, 24 10:39 PM
Dec 09, 24 01:08 AM
Dec 08, 24 11:19 PM
Dec 07, 24 03:38 PM
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.