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
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)
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 )