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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

 Apr 30, 2019
 #1
avatar+100586 
+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)

 

 

cool cool cool

 Apr 30, 2019
 #2
avatar+100586 
+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  = 3PN

 

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 )

 

 

 

cool cool cool

 Apr 30, 2019

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