Finding coordinates

[JustDanny]

Hello everyone.

















- We know the coordinates of (x,y) and (v,w).
- (m1, m2) is the mid-point of (x,y) and (v,w).
- The distance between the mid-point and (a,b) is 1.45.
- d is the distance between (a,b) and (x,y).

With this data, I can calculate the distance between (x,y) and the coordinates of the midpoint. After knowing that, I can just use the c^2=h^2+h^2 rule in order to find the value of d. Now my question is how do I find out the coordinates of (a,b) in the simplest way possible?

Thanks!

 

[Dr.Peterson]

Hello everyone.

















- We know the coordinates of (x,y) and (v,w).
- (m1, m2) is the mid-point of (x,y) and (v,w).
- The distance between the mid-point and (a,b) is 1.45.
- d is the distance between (a,b) and (x,y).

With this data, I can calculate the distance between (x,y) and the coordinates of the midpoint. After knowing that, I can just use the c^2=h^2+h^2 rule in order to find the value of d. Now my question is how do I find out the coordinates of (a,b) in the simplest way possible?

Thanks!

I'm not sure what you mean by "c^2=h^2+h^2"; what are c and h?

But you can find d using the Pythagorean theorem with legs 1.45 and the distance from (x,y) to (m1,m2).

On the other hand, the simplest way to find (a,b) depends on what you have learned. I myself would probably use vectors, without finding d at all. If you don't know enough about them, you might write the equation of the green line, and find a point along it at the right distance.

Another question though, is whether you know the relative directions. Could (a,b) be in the other direction along that same line?

 

[JustDanny]

I'm not sure what you mean by "c^2=h^2+h^2"; what are c and h?

But you can find d using the Pythagorean theorem with legs 1.45 and the distance from (x,y) to (m1,m2).

On the other hand, the simplest way to find (a,b) depends on what you have learned. I myself would probably use vectors, without finding d at all. If you don't know enough about them, you might write the equation of the green line, and find a point along it at the right distance.

Another question though, is whether you know the relative directions. Could (a,b) be in the other direction along that same line?

Hey,

"c^2=h^2+h^2" is a reference to the Pythagorean theorem, I just used that odd notation. My bad!

I did learn about vectors so that would be a possibility! But if possible, could you also present me the green line equation solution?

Yes, (a,b) could be in the other direction along the same line.

Thank you!

 

[Dr.Peterson]

"c^2=h^2+h^2" is a reference to the Pythagorean theorem, I just used that odd notation. My bad!

I did learn about vectors so that would be a possibility! But if possible, could you also present me the green line equation solution?

Yes, (a,b) could be in the other direction along the same line.

No, I don't "present" completed solutions; I suggest them, and then help you (if you need it) along the way.

Using vectors, how might you find the vector from (m1,m2) to (a,b)? Might it help to rotate a known vector 90 degrees?

As for the line, how might you write an equation for it? Might the point-slope form be useful?

And if (a,b) could be on either side, then you will get two solutions. That might come from a quadratic equation at some point.

Does that give you ideas? Show me some work, and I can have more to say.

 

[Steven G]

Where does it say that the green line meets the black line at a right angle? This is clearly something that I would not assume unless it is given.

 

[Dr.Peterson]

That's funny ... I thought I recalled that it did say that. If not, then I don't think it's solvable.