# Thread: Find the coordinates of the point Q given these conditions...

1. ## Find the coordinates of the point Q given these conditions...

Given

X = <-1, 2>, Y = <5, 5>, Z = <2, -1>.

Q is on the segment YZ where the length of the segment YQ is double the length of the segment QZ.

I'm trying to do this without calculating any lengths.

Looks like something to do with a linear combination of vectors.

2. ## Re: Find the coordinates of the point Q given these conditions...

Actually, I thought of...

Let Q = <x, y>

YZ = 2(QZ)

<x - 5, y - 5> = 2<2 - x, -1 - y>

x = 3, y = 1

Q = <3, 1>

YQ = <-2, -4>

TZ = <-1, -2>

||YQ|| = 20^(1/2)

||QZ|| = 5^(1/2)

I avoided using lengths until the end to make a check on this. Seems correct.

3. ## Re: Find the coordinates of the point Q given these conditions...

Correction

Actually, I thought of...

Let Q = <x, y>

YQ = 2(QZ)

<x - 5, y - 5> = 2<2 - x, -1 - y>

x = 3, y = 1

Q = <3, 1>

YQ = <-2, -4>

QZ = <-1, -2>

||YQ|| = 20^(1/2)

||QZ|| = 5^(1/2)

That looks right.