PROBLEMS ON SECTION FORMULA

Problem 1 :

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 are:

A) (2, 4)     B) (3, 5)      C) (4, 2)        D) (5, 3)

Solution:

Let P(x, y) divides line segment joining A(1, 3) and B(4, 6) in the ratio 2 : 1.

The coordinates of a point (x, y) dividing the line segment joining the points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ are given by

Thus, (3, 5) divides the line segment AB in the ratio 2 : 1.

So, option (B) is correct.

Problem 2 :

The point P which divides the line segment joining the points A(2, -5) and B(5, 2) in the ratio 2 : 3 lies in the quadrant 

A) I     B) II       C) III      D) IV

Solution:

The point P divides the line segment joining the point A (2, -5) and (5, 2) in the ratio 2: 3.

So, option (D) is correct.

Problem 3 :

If C is a point lying on the line segment AB joining A(1, 1) and B(2, -3) such that 3 AC = CB, then find the coordinates of C.

Solution:

The coordinates of the given points are A(1, 1) and B(2, -3).

3AC = CB

AC : CB = 1 : 3

The point C divides the line segment AB in the ratio 1 : 3.

By using section formula,

Problem 4 :

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that PA/PQ = 2/5. If point P also lies on the line 3x + k(y + 1) = 0, find the value of k.

Solution:

Let the coordinates of A be (x, y).

Let (x, y) be the coordinates of A which divides PQ in the ratio 2 : 3 internally.

By using section formula, we get

Now, the point (2, -4) lies on the line 3x + k(y + 1) = 0

3(2) + k(-4 + 1) = 0

6 - 3k = 0

3k = 6

k = 6/3

k = 2

Problem 5 :

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7AB, where P lies on the segment AB.

Solution:

The coordinates of point A and B are (-2, -2) and (2, -4).

AP : PB = 3 : 4

Point P divides the line segment AB in the ratio 3 : 4.

Problem 6 :

A point P divides the line segment joining the points A(3, -5) and B(-4, 8) such that AP/PB = K/1. If P lies on the line x + y = 0, then find the value of K.

Solution:

The given points are A(3, -5) and B(-4, 8).

Here x₁ = 3, y₁ = -5, x₂ = -4 and y₂ = 8.

By using section formula,

Thus, the required value of K is 1/2.