Question

The line 7x - 8y = 4 divides join of (-8,-4) and (6,k) in the ratio of 2 : 5. Find the value of k.

Answer 1

Let the point of intersection of AB and the line 7x-8y=4, be the point P (a,b)

Also, given the line 7x-8y = 4 divides the line segment AB in the ratio 2 : 5.

i.e. AP: PB = 2: 5

Coordinates of P are,

P (a,b) = P `((12 - 40)/7 , (2"k" - 20)/7) = "P" (-4, (2"k" - 20)/7)`

P (a,b) lies on the line 7x - 8y = 4,

P will satisfy the equation of the line

7(-4) - `((2"k" - 20)/7)` = 4

-8 `((2"k" - 20)/7)` = 32

2k - 20 = -28

2k = -8

k = -4