Math question, please help me out! All answers are very greatly appreciated!! ?

Question

So if you're reading this, I really appreciate that you're going to try to help me. You have no idea. So I'm taking Geometry this year and this is a class two years ahead of my grade and I need a little help with my homework.

The instructions say: Given the coordinate of one of the endpoints of line AB and its midpoint M, find the coordinates of the other endpoint.

The first problem says A(0,9), M(2,5)

Anyone want to explain how I'm supposed to do this. I don't need the answer, just how to do it and I'll figure it out myself. I know if i ask for the answer as well someone is going to tell me to do my own homework so if you're going to say that please go away because I'm trying really hard and this is the first part of my homework I really really truly don't get. Anyways, thanks for any help you may give me. And for all the answers. If you need any more information please ask and I'll see what I can do. Thanks again [:

Answer 1

since the midpoint is halfway between one endpoint and the other, all you need to do is take the difference between the coordinates of M and A and add that result to M

In your example: M-A=(2,5)-(0,9)=(2,-4)

                         (2,-4)+(2,5)=(4,1)=B

Answer 2

In problems involving coordinate geometry it is alway useful to make a sketch. In this case plot A at coordinates {0, 9} and M at coordinates {2, 5}. Since M is the midpoint of AB then clearly B must be located 2 additional units positively along the x-axis and 4 units in the negative direction along the y-axis with respect to M.

I must continue in order to make the point here.

The point B is thus at coordinates {4,1}.

Is this correct?

The formula for mid points is as follows:-

x = [x1 + x2]/2 ; y = [y1 + y2]/2  where {x,y} is the Mid Point and

{x1,y1} is say A and {x2,y2} is say B  in other words A and B are the end points of the line

Thus in our case A is {0,9} and we believe B to be {4,1} what is the mid point.

It is x = [0+4]/2  = 2

and y = [9+1]/2  = 5

That is to say Mid Point is given by the coordinates {2,5} which is what we were given.

Answer 3

so basically picture a straight line with three points (2 end points and one middle point)

one end point(0,9) the mid point is (2,5)

so basically here u r going 2 steps in the x axis which is half of wat u shud be going

similarly u are going 4 steps DOWN the y axis which is again half of wat u r suppposed to be going

so wat i am telling is that treat each part of the coordinate different

A(0)-----> M(2)------>B(?)

A(9)------>M(5).......>B(?)

remmeber m is half way to B

therefore answer is (4,1)

Answer 4

Draw your line from A to M then extend it for the same distance along the same trajectory.

Answer 5

Suppose B has coordinates (x,y).  The midpoint of AB = ((0+x)/2,(9+y)/2).  But since the midpoint is M, we know that (0+x)/2 = 2 and

(9+y)/2 = 5.  Solving these we find x = 4 and y = 1, so M = (4,1).