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  1. Given the points A(-3,-4) and B(5,0), find the coordinates of point P on the directed line segment AB that partitions AB in the ration 2:3. 
  2. Given J(-2,5) and k(2,-3). Find the point P on JK such that 4•JP=PK. 
 Dec 6, 2018

Now this is something I can help with!

#1: The ratio 2:3=5 so you would use 2/5 or 3/5 as a fraction (I'll do 2/5 with this example)

Use the distance formula: [x1+a/a+b(x2-x1), y1+a/a+b(y2-y1)]

Plug in all the numbers and solve: 

X: -3+2/5(5+3)=0.2

Y: -4+2/5(0+4)=-2.4

P= (0.2,-2.4)

Now #2 is a bit different but also the same. 

The ratio would be 4:1. Four part JP and one part PK.

4:1=5 so your fraction would be either 4/5 or 1/5 (using 1/5 here)

X: -2+1/5(2+2)=-1.2

Y: 5+1/5(5+3)=6.6


Tell me if you don't understand something from my explanation and I can try to help a little bit more.

 Dec 6, 2018

Thank you so much! I think I understand, if I have any questions I'll make sure to ask. 

Bleh674  Dec 6, 2018

You're very welcome! I'd love to help if you have anymore of these questions ^-^

RainbowPanda  Dec 6, 2018

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