FIND THE RATIO THAT THE POINT DIVIDES THE LINE SEGMENT

Problem 1 :

Find the ratio in which the point (11, 15) divides the line segment joining the point (15, 5) and (9, 20).

Solution:

Given points are (15, 5) and (9, 20).

Let P(11, 15) divide AB internally in the ratio l : m.

By the section formula,

Equating the coefficients of x, we get

Hence, the point divides the line segment joining the points in the ratio 4 : 2.

Problem 2 :

Find the ratio in which the point P(m, 6) divides the line segment joining the point A(-4, 3) and B(2, 8). Also find the value of m.

Solution:

Using the section formula, if a point (x, y) divided the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio l : m, then

Let P divides the join of A and B in the ratio k : 1, then

Therefore, we have

Problem 3 :

Find the ratio in which the point P(-6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a.

Solution:

Using the section formula, if a point (x, y) divided the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio l : m, then

l : m = 3 : 2

To find a, equating the coefficient of y

Problem 4 :

Find the ratio in which the point P(-3, a) divides the join of A(-5, -4) and B(-2, 3). Also find the value of a.

Solution:

Using the section formula, if a point (x, y) divided the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio l : m, then

To find a, equating the coefficient of y

Problem 5 :

Find the ratio in which the point P(a, 1) divides the join of A(-4, 4) and B(6, -1). Also find the value of a.

Solution:

Using the section formula, if a point (x, y) divided the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio l : m, then

To find a, equating the coefficient of x

Problem 6 :

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Solution:

Hence, the point divides the line segment joining the points in the ratio 2 : 7.