Points on a line

[mkx2000]

I'm writing this from memory:

Three points X, Y, Z are on a line k, a forth point W is not on k. When WX = WZ, which of the following must be true:

[ 5 Answers in the form of inequalities: WY > WX, etc ]

My question is: What does WX mean? Scalar product of W and X? Length of vector WX?

I was totally confused by this question (came on my GMAT, so I don't know the exact answer choices anymore and don't have an OA). I didn't find a correct answer with scalar product, and then tried length. Wasted a lot of time on this question .

Maybe someone can shed a light on how to solve this.

Thanks

[bkparikh]

Without knowing the answer choices this is difficult to solve, however in most cases WX would refer to the length of the line segment.

Do you know if Y was between X and Z on line k?

[mkx2000]

Yeah, I forgot that of course, Y is between X and Z on the line.

It does make more sense with length, so thats probably it.

[bkparikh]

If Y is between X and Z then WX > WY and WZ > WY. Think of an isosceles triangle where WXZ where the base is XZ and point Y is on the base. WY must be shorter than the sides (WX and WZ).

[mkx2000]

Thanks!

Thats what I tought at the end (though I'm not sure whether I got it right, since I was quite confused at that point).

[hrif]

consider O the center of XZ

(OX)2 + (OW)2 = (XW)2
(CY)2 + (OW)2 = (YW)2

Since CX>OY then XW>YW