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, -(12)/(5) )` partitions AB

Let's assume it partitions into m:n

so, we get

`(AP)/(PB)=(m)/(n)`

so, we can write our point as

`(-1,-(12)/(5) )=((2m-3n)/(m+n),(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= (2m-3n)/(m+n)`

`-(12)/(5) =(0m-4n)/(m+n)`

now, we can solve for m/n

`-m-n=2m-3n`

`3m=2n`

`(m)/(n) =(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=((10-4)/(2),(-2+6)/(2))`

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