Question

Help!!! On geometry all help is appreciated

Answer 1

(1)

we are given two points

A=(-3,-4)

B=(2,0)

and point P $(-1, -\frac{12}{5} )$ partitions AB

Let's assume it partitions into m:n

so, we get

$\frac{AP}{PB}=\frac{m}{n}$

so, we can write our point as

$(-1,-\frac{12}{5} )=(\frac{2m-3n}{m+n},\frac{0m-4n}{m+n})$

now, we can set x-value to x-value

and y-value to y-value

and then we can solve for m and n

$-1= \frac{2m-3n}{m+n}$

$-\frac{12}{5} =\frac{0m-4n}{m+n}$

now, we can solve for m/n

$-m-n=2m-3n$

$3m=2n$

$\frac{m}{n} =\frac{2}{3}$

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

$M=(\frac{10-4}{2},\frac{-2+6}{2})$

$M=(3,2)$............Answer