Question

if the ratio in which the joining of points (-3,10) and (6,-8) is divided by the point (-1,6)

Answer 1

I am adding a picture u can see the solution of your Question in it

Answer 2

Let,
A-(-3,10)
B-(6,-8)
And point(p) divides AB in the ratio AP/PB = m/n
By section formula
P(x,y)= p(mx2+nx1 ÷ m+n,my2+ny1 ÷ m+n)
=p(-1,6) = p( m × 6 + n × -3 ÷ m + n, m × -8 + n × -10 ÷ m+ n)
=p ( -1 , 6 ) = p ( 6m -3n ÷m+n, -8m -10n ÷ m + n )
= 6m - 3n ÷ m + n = -1 , -8m -10n ÷ m + n ÷ m+ n = 6
=6m - 3n ÷ m + n = -1
=6m - 3m = -m-n
= 6m +m = 3m -n
=7m = 2n
=m/n = 7/2
U can find the other one by same process...
I may make mistake check once nicely