Geometry; find endpoint from midpoint to endpoint

Question

The midpoint of AB is M3 and -3 if the coordinates of a is two and -8 what are the coordinates of b

Answer 1

Hi Nalia, it looks like this question is asking about a xy graph, right? So you are given two points, M which is (3, -3) and A which is (2, -8) and you're asked to find the coordinates of point B.

They tell us that M is the midpoint between A and B, meaning that the line goes from A to M, having traveled a certain distance horizontally and a certain distance vertically, and then -- because midpoints are in the exact middle, and have the same distance on both sides -- the line goes straight on from M to B. It will travel that SAME distance horizontally and vertically. This is really cool because we don't even have to use the Distance Formula of √ [ (x₂-x₁)² + (y₂-y₁)² ] -- we don't need it! We can think about the question like this:

From A to M, the x-coordinate (horizontal distance) changes from 2 to 3. So it moved in the positive direction by 1 unit. From M to B, the x-coordinate will also change by positive 1 unit. So it will change from M's x-coordinate of 3, to a new x-coordinate of 4.

Now we do the same thing for the y-coordinate (vertical distance): from A to M, it changes from -3 to -8. So it moved in the negative direction (downwards, like a subtraction) by 5 units. So from M to B, the y-coordinate will again change by negative 5 units, and we can find the new y-coordinate by subtracting 5 from -8. Once you have found that number, -8 - 5, you will know your new y-coordinate for point B.

Then, just write down the x-coordinate and y-coordinate that we calculated, and you will know where point B is!

If you get stuck or want to know more about the "why" of any part of this answer, let me know and I'll be happy to help you out!