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:

**Answers:**

**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**

**Distance Formula****Distance Properties in some Geometrical Figures****Conditions of Collinearity of Three Points****Problems on Distance Formula****Distance of a Point from the Origin****Distance Formula in Geometry****Section Formula****Midpoint Formula****Centroid of a Triangle****Worksheet on Distance Formula****Worksheet on Collinearity of Three Points****Worksheet on Finding the Centroid of a Triangle****Worksheet on Section Formula**

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