1. Given J(-2, 5) and K(2, -3). Find the point P on JK such that 4·JP = PK.

2. Given M(5, -2) and N(-5, 3). Find the point P on MN such that MP = 3·PS

I can't figure this out. I've tried but I don't understand. Please help and show work! Thanks

Guest Apr 30, 2019

#1**+1 **

1. Given J(-2, 5) and K(2, -3). Find the point P on JK such that 4·JP = PK.

J 1 P 4 K

We can divide JK into 5 equal segments......and PK is 4 of these....so....P is (1/5) of the distance from J to K

So....we can find P as follows

P = [ ( -2 + (1/5)(2 - -2) , 5 + (1/5) (-3 - 5) ] =

[ -2 + (1/5) (4) , 5 + (1/5)(-8) ] =

[ -2 + 4/5 , 5 - (8/5) ] =

( - 10/ 5 + 4/5 , 25/5 - 8/5 ) =

( - 6/5 , 17/ 5)

CPhill Apr 30, 2019

#2**+1 **

2. Given N(-5, 3) and M (5, -2). Find the point P on MN such that MP = 3·PS

N 1 P 3 M

I'm assuming that you mean MP = 3P**N**

Like the last one, MN can be divided into 4 equal parts.....and MP is 3 of them......so...P is (1/4) of the way between M and N......so we have

P =

[ -5 + (1/4)(5 - - 5) , 3 + (1/4)(-2 - 3) ] =

[ -5 + (1/4)(10) , 3 + (1/4)(-5) ] =

[ - 5 + 10/4 , 3 - 5/4 ] =

[ -20/4 + 10/4, 12/4 - 5/4 ] =

[ - 10/4, 7/4 ] =

(-5/2, 7/4 )

CPhill Apr 30, 2019