Question

A(-3, 6), B(2, 1). If 'p' divides AB in the ratio 3:2 internally and the point '
p lies on the line
3x - 8y + k = 0, find 'k'​

Answer 1

Answer:

Let the coordinate of p be p(a,b)

we know,

p(a,b) = (mx2 +nx1)/m+n ,( my2 + ny1)/m+n

WHERE m = 3 and n= 2

a = 3.2 +2.(-3)/2

or, a= 6 -6 /2

or a=0

again,

b = 3.1+ 2.6/2

or, b = 3+12 /2

or, b= 15/2

so,

p(a,b) = p(0,15/2)

as p lies on the line having equation

3x +8y +k =0

3*0 +8*15/2 +k = 0

4*15 + k =0

k = -60