Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line

Solution:

Let AB be the line segment between the axes such that point R (h, k) divides AB in the ratio 1: 2.

Let the respective coordinates of A and B be (x,0) and (0, y) .

Since point R (h, k) divides AB in the ratio 1 : 2, according to the section formula,

(h, k) = [(1 (0) + 2 (x))/(1 + 2), ((1 (y) + 2 (0))/(1 + 2)

(h, k) = (2x/3, y/3)

h = 2x/3, k = y/3

x = 3h/2, y = 3k

Therefore, the respective coordinates of A and B are (3h/2, 0) and (0, 3k)

Now, the equation of the line AB passing through points (3h/2, 0) and (0, 3k) is

(y -0) = [(3k - 0)/(0 - 3h/2)] [x - 3h/2]

y = - 2k/h (x - 3h/2)

hy = - 2k (2x - 3h)/2

hy = - k (2x - 3h)

hy = - 2kx + 3kh

2kx + hy = 3kh

Thus, the required equation of a line is 2kx + hy = 3kh

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NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 19

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.

Summary:

The equation of the line that corresponds to the line segment which is divided by the point R (h, k) in the ratio 1 : 2 is 2kx + hy = 3kh