Conditions of t with the correct geometrical object:

S

Sam007

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Hi guys,

This is for the extension section of my course. There are similar questions I have to do. Can anyone please help me on how to do this question so I can solve similar questions?Thanks:)

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I would start by determining where x will be for t = 0, -1, and -1/2. Presumably you see that x will lie on the line AB; knowing these three points will guide you in answering the questions. (One of them will be A, one will be B, and another will be somewhere else -- as you can tell from the options, it will be the point midway between them.)

Please tell us what you find, and what your conclusions are, so we can help if you are wrong.
 
When t=0 then x= vector B
t=-1 then x= vector a
when t=-1/2 then 2x= vector A +vector b
 
I hope you see that 2x= A + B means that x is the midpoint of AB. Do you?

You know that when t = -1, x = A. You can see by example (and can prove) that when t increases above -1 (e.g. -1/2, 0), x is moving toward B, right? So what is the set of all x for t > -1? Which of the four figures is this?
 
Ahh, I see.

So for values of 0<t<-1. It would be Segment AB (4)

When t>-1/2. It would be 2. Because we are in-between B and X

When t<0 is 1 as we are getting farther away from B

When T>-1. We are now in between A and X (3)

Is that a correct interpretation?
 
Sam007 said:
So for values of 0<t<-1. It would be Segment AB (4)

When t>-1/2. It would be 2. Because we are in-between B and X

When t<0 is 1 as we are getting farther away from B

When T>-1. We are now in between A and X (3)

Is that a correct interpretation?
Click to expand...

The first is correct, and if you meant -1<t<0, not 0<t<-1, which is empty.

The second is wrong; if by X you mean the midpoint of AB; set #2 has nothing to do with that point. And you meant t < -1/2, right?

The third is correct, though "farther from B" is not clear, as that would be true in either direction.

The fourth is wrong; t > -1 has nothing to do with X.

The trickiest set is #2, which is stated in a complicated way. Sketch out what part of the line that would be, before you assign an interval to it.
 
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