# Homework Help: Abstract geometry I think

1. Dec 28, 2011

### mtayab1994

1. The problem statement, all variables and given/known data

(E) is a group of points M from a level/plane

$$MA^{2}-MB^{2}=-4$$ And I is the center of [AB]

2. Relevant equations

show that IM*AB=-2 ( IM and AB have arrows on top)

3. The attempt at a solution

Well i split $$MA^{2}-MB^{2}=(MA-MB)(MA+MB)$$

then i got : $$MA^{2}-MB^{2}=BA*(MA+MB)$$

and i don't know where to go on from there any help?

Last edited: Dec 28, 2011
2. Dec 28, 2011

### Staff: Mentor

This doesn't make any sense to me.

What is A? What is B? Is AB the line segment from point A to point B?

3. Dec 28, 2011

### mtayab1994

My fault AB is a line segment and I is the center of it.

4. Dec 28, 2011

### SammyS

Staff Emeritus
I think this is impossible! $MA^{2}+MB^{2}=-4$

Do you mean? $MA^{2}-MB^{2}=-4$

5. Dec 28, 2011

### mtayab1994

Yea sorry my fault that was a typo its MA^2-MB^2=-4

6. Dec 28, 2011

### mtayab1994

Any ideas?

7. Dec 28, 2011

### Staff: Mentor

What does this mean?
Does * represent the dot product?

8. Dec 28, 2011

### mtayab1994

Yes.

9. Dec 28, 2011

### SammyS

Staff Emeritus
Since "IM and AB have arrows on top", and "AB is a line segment", I take it that these are all vectors and, for example, $\vec{MB}$ is a vector from point M to point B.

If that's the case, then notice that $\vec{MA}=\vec{MI}+\vec{IA}\,.$ Do similar for $\vec{MB}$

Notice that$\vec{IB}=-\vec{IA}\,.$

Now look at $\vec{MA}+\vec{MB}$ again.