(1)
we are given two points
A=(-3,-4)
B=(2,0)
and point P [tex](-1, -\frac{12}{5} )[/tex] partitions AB
Let's assume it partitions into m:n
so, we get
[tex]\frac{AP}{PB}=\frac{m}{n}[/tex]
so, we can write our point as
[tex](-1,-\frac{12}{5} )=(\frac{2m-3n}{m+n},\frac{0m-4n}{m+n})[/tex]
now, we can set x-value to x-value
and y-value to y-value
and then we can solve for m and n
[tex]-1= \frac{2m-3n}{m+n}[/tex]
[tex]-\frac{12}{5} =\frac{0m-4n}{m+n}[/tex]
now, we can solve for m/n
[tex]-m-n=2m-3n[/tex]
[tex]3m=2n[/tex]
[tex]\frac{m}{n} =\frac{2}{3}[/tex]
so, option-C.........Answer
(2)
we are given points as
J=(10, -2)
N=(-4 ,6)
Let's assume mid-point between J and N as M
so, we get
[tex]M=(\frac{10-4}{2},\frac{-2+6}{2})[/tex]
[tex]M=(3,2)[/tex]............Answer
