Question

A directed line segment from A(-8, -8) to B is divided by P(2, 0) in a ratio 2:1. Where is B?

a.) (22,16)
b.) (12,8)
c.) (7,4)

Answer 1

Alright so the ratio 2:1 information means the distance from A to P is 2x the distance from P to B, right?

Answer 2

So there is more than one way to do this

Answer 3

Okie dokie!

Answer 4

do you know the distance formula?

Answer 5

Yupp!

Answer 6

@caseyrt How do I apply the distance formula to this problem?
By using the distance formula, I got 2 from those given points.

Answer 7

ok sweet so first thing to do is find the distance from A to P.

Answer 8

Okie dokie is 2 correct? =)

Answer 9

P(2, 0) A(-8, -8) is that right?

Answer 10

Yes that's right : )

Answer 11

so our change in x is 10 and change in y is 8. So we should have \[\sqrt{10^2+8^2}\] right?

Answer 12

yes!
\[\sqrt{100+64}\]

right?

Answer 13

yah there we go

Answer 14

then....

= \[\sqrt{164}\]

Answer 15

ok so the distance from P to B is going to be 1/2 that

Answer 16

or \[\sqrt{41}\] because you square the 1/2 when you take it inside the radical

Answer 17

so set up the distance formula equation from P to B, just use x and y for the B points, and set it equal to sqrt(41)

Answer 18

All right, makes sense!

Answer 19

and then you can make an equation for the line you're on in y=mx+b form and sub in the "mx+b" part for y in your expression and solve for x. Then, put x back into the equation you have for your line and solve for y
make sense?

Answer 20

Yes! Wow thank you!

Answer 21

you bet!