Find the ratio in which the line segment pq, where p (4, -2) and q (1, 3), is divided by the x-axis.

Practice the questions given in the worksheet on section formula.

To find the co-ordinates of a point which divides the line segment joining two given points in a given ratio.

1. Find the coordinates of the points which divides the join of P (-1, 7) and Q (4, -3) in the ratio 2 : 3.

2. Find the point of bisection of the line segment AB, where A (-6, 11) and B (10, -3)

3. Find the coordinates of the points which divides the join of X (-1, 7) and Y (4, -3) in the ratio 7 : 2.

4. Find the point of trisection of the line segment AB, where A (-6, 11) and B (10, -3).

5. Find the coordinates of points of trisection of the line segment joining the point (6, -9) and the origin.

6. If X, Y and Z divides the line segment PQ in four equal parts such that PX = XY = YZ = ZQ, and the coordinates of P and Q are (1, 6) and (3, -4) respectively then find the coordinates of X, Y and Z.

7. In what ratio is the line segment joining X (0, 3) and Y (4, -1) divided by the x-axis. Write the coordinates of the point where XY intersects the x-axis.

8. If the point (p, q) is the middle point of the line segment joining the points P (7, -4) and Q (-1, 2) then find p and q.

9. Let M (-3, 5) be the middle point of the line segment XY whose one end has the coordinates (0, 0). Find the coordinates of the other end.

10. In what ratio is the line segment joining X (2, -3) and Y (5, 6) divides by the x-axis? Also, find the coordinates of the point of division.

11. The coordinates of the midpoint of the line segment AB are (1, -2). The coordinate of A are (-3, 2). Find the coordinate of B.

12. Find the ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis.

13. Find the ratio in which the point X (-6, h) divides the join of P (-4, 4) and Q (6, -1) and here hence find the value of h.

14. Find the ratio in which the line segment PQ, where P (4, -2) and Q (1, 3), is divided by the x-axis.

Answers for the worksheet on section formula are given below:

1. (1, 3)

2. (2, 4)

3. (2, -3)

4. ($$\frac{4}{3}$$, -$$\frac{4}{3}$$), ($$\frac{8}{3}$$, -$$\frac{8}{3}$$)

5. (4, -6) and (2, -3)

6.  X ($$\frac{3}{2}$$, $$\frac{7}{2}$$), Y (2, 1) and Z ($$\frac{5}{2}$$, -$$\frac{3}{2}$$)

7. 3 ; 1; (3, 0)

8. p = 3, q = -1

9. (-6, 10)

10. 1 : 2; (3, 0)

11. (5, -6)

12. 5 : 2

13. 3 : 2; h = 2

14. 2 : 3

Distance and Section Formulae

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Find the ratio in which the line segment joining P ( 4, -6) and Q ( -3, 8) is divided by the line y = 0.

Given PQ is divided by the line Y = O i.e. x-axis.

Let S (x, O) be the pcint on line Y = 0, which divides the line segment PQ in the ratio k : 1.

Coordinates of S are

x = (-3"k" + 4)/("k" + 1) ,   0 = (8"k" - 6)/("k" + 1)

⇒ 8 k = 6

⇒ k = 3/4

Hence, the required ratio is 3: 4.

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Page 2

In what ratio is the line joining (2, -1) and (-5, 6) divided by the y axis ?

Let the point P (0, y) lies on y-axis which divides the line segment AB in the ratio k : 1.

Coordinates of P are ,

0 = (-5 "k" + 2)/("k" + 1) ,  "y" = (6"k" - 1)/("k" + 1)

⇒ 5 k = 2

⇒ k = 2/5

Hence, the required ratio is 2 : 5.

Is there an error in this question or solution?