a point P divides the line segment joining the points A ()3,-5 B (-4,8) such that ap/pb= k/1 - Maths - Coordinate Geometry

Question

a point P divides the line segment joining the points A ()3,-5 B
(-4,8) such that ap/pb= k/1 if P lies on the line x+ y =0 then find
the value of k

Ayush Jha · Accepted Answer

We have a point P which divides the line segment joining A(3,-5) and B(-4,8) in the ratio k:1

So apply the section formula in order to get,

$P (x, y) = (\frac{- 4 k + 3}{k + 1}, \frac{8 k - 5}{k + 1})$

Since this point P lies on the line x+y=0

So,

$\frac{- 4 k + 3}{k + 1} + \frac{8 k - 5}{k + 1} = 0 4 k - 2 = 0 k = \frac{1}{2}$

a point P divides the line segment joining the points A ()3,-5 B (-4,8) such that ap/pb= k/1 .if P lies on the line x+ y =0 then find the value of k