Question

How do I find this point? http://prntscr.com/agnnoc

Answer 1

I can find the distance of a just fine, but I have no idea how to get the actual point it lands on if it were "extended" 2/3 a.

Answer 2

It appears to me that the vector from (0,-4) to (3,0) is <3,4>. Do you agree with this?

Answer 3

Those points I gave were an example to help me understand it better, but yes I would agree.

Answer 4

All right. The vector in the direction opposite to <3,4> is (-2/3)<3,4>. If you agree, find this new vector. If you disagree, present another approach.

Answer 5

Hmm, so would the point I am trying to find just be <x, y> -> (2/3x, 2/3y)?

Answer 6

No. I'll go into that in a moment. Please decide where you stand and respond to my previous post.

Answer 7

I'm not sure if I agree... In your best opinion, could I use this to find my point?

Answer 8

If you don't agree, come up with an alternative. Our goal is to find the vector from (0,-4) to the unknown point. Since you don't know the coordinates of that point, let the point be (x,y).

Answer 9

Also, I ask you to agree or disagree with the statement: "The two vectors shown are collinear (on the same line).

Answer 10

Oh yes, I was confused, but yes they have the same slope and are collinear

Answer 11

So I would agree :)

Answer 12

Assuming that the vectors shown in the illustration are collinear, then the unknown point can be found by vector addition. But first we must have two vectors to add. One is<3,4>. How would we go about finding the vector (-3/4)<3,4>?

Answer 13

I don't really know. I haven't had much experience with vectors. All of this is for a personal computer program I am trying to make...

Answer 14

Difficult situation to be in. We usually learn things more efficiently if we do so in a linear fashion: first things first. Have you any experience with vector addition?

Answer 15

nope

Answer 16

Certainly we can finish this problem, but I'm a bit wary of starting from scratch to explain vector addition and subtraction if you haven't studied either yet.

Have you found the length of vector a ?

Answer 17

I'm sorry but I really don't know anything about vectors. We can keep in touch, and I can learn more about them and return to this question if you'd like?

Answer 18

I'd be happy to do that. That's a very reasonable and fair proposition.
So y ou have something to compare your answer to: the distance between (0,-4) and (3,0) is 5. See whether you can duplicate this result.

Answer 19

Yes the two legs are 4 and 3, so the hypotenuse must be 5.

Answer 20

Note that you could multiply this distance by (3/4) to obtain the distance from (0,-1) to the unknown point (x,y).

Answer 21

Right on that 3^2 + 4^2 =5^2. Very good.

Answer 22

So the distance between (x, y) and (0, -4) must be 3 1/3 units then?

Answer 23

Because the distance between those two points is just 2/3 that distance.

Answer 24

Yes. Does this give u enuf info from which to determine x and y?

You could do this graphically to obtain a preliminary estimate.
On a set of coord. axes, draw vector a (whose length is 5).
Next, start at (0,-1) and draw the new vector that you have just proposed. It must line on the same line as does the given vector a.

Where this new vector ends, in the 3rd quadrant, the x- and y-coordinates should be more or less obvious; at least, you could obtain a good estimate for (x,y).

Answer 25

If you could solve this problem graphically and through algebra and/or vector addition, that'd be super.

Answer 26

I'm having trouble finding out what the vector is... How do you find a vector?

Answer 27

Must you use vectors for your computer program? If you have little or no experience with vectors, perhaps a different topic for your computer program would be appropriate.

Answer 28

Ok, so it is as simple as I thought.

Answer 29

The vector would just be the legs in the x and y direction