Question

find the ratio in which the point [-3,k] divides the segment joining the points [-5,-4] and [-2,-3]

Answer 1

Answer:

Step-by-step explanation:

A        n              P            1               B      

.____________._____________.

(- 5, - 4)          (- 3, k)                       (- 2, 3)

Let the ratio in which P divides AB be n : 1.

Considering x co-ordinate for section formula

⇒ - 3 = (- 2)n + 1( - 5)/n + 1

⇒ - 3(n + 1) = - 2n - 5

⇒ - 3n - 3 = - 2n - 5

⇒ 5 - 3 = 3n - 2n

⇒ 2 = n

Therefore,

⇒ n/1 = 2/1

or, n/1 = 2 : 1

Then,

Considering y co-ordinate

⇒ k = 2(3) + 1(- 4)/2 + 1

⇒ k = 6 - 4/3

⇒ k = 2/3

Hence, the value of k is 2/3.