Find the Coordinates of B

[Amy12345_1000]

If the coordinates of A are (1,1) and the midpoint of line AB is (2,0) then the coordinates of B are..... A. (-0.5,0.5) B. (0.5,0.5) C. (-1,0) D. (-5,-1)

 

[Mrspi]

If the coordinates of A are (1,1) and the midpoint of line AB is (2,0) then the coordinates of B are..... A. (-0.5,0.5) B. (0.5,0.5) C. (-1,0) D. (-5,-1)

What have you done to start this problem?

You might want to review the relationship between the coordinates of the MIDPOINT of a segment and the coordinates of the endpoints of the segment.

The midpoint formula should be of some assistance.... To find the midpoint of a segment whose endpoints are known, ADD the x coordinates of the endpoints and divide by 2 to get the x coordinate of the midpoint; ADD the y-coordinates of the endpoints and divide by 2 to get the y-coordinate of the midpoint.

That is, if (x₁, y₁) and (x₂, y₂) are the endpoints of a segment AB, you'd find the coordinates of the midpoint this way:

(x₁ + x₂)/2 would be the x-coordinate of the midpoint.

(y₁ + y₂)/2 would be the y-coordinate of the midpoint.

In your problem, you KNOW that one endpoint has coordinates (1, 1). And you KNOW that the midpoint has coordinates (2, 0). You're looking for the coordinates of the other endpoint of the segment. Let (x, y) be the coordinates of the other endpoint....

Then, we know that the x-coordinate of the midpoint is (1 + x)/2, and we also know that x-coordinate is 2. SO.......

(1 + x) / 2 = 2

Solve that for x, and you'll have the x-coordinate of the other end of the segment.

Do something similar to find the y-coordinate of the other end of the segment.

If you're expecting that someone is going to hand you an answer without seeing any work on your part, you've come to the wrong place. If you show us what you've done, and tell us where/why you are "stuck," we'll do our best to try to help you.

 

[soroban]

Hello, Amy12345_1000!

There must be a typo . . . the answer is not listed.

If the coordinates of A are (1,1) and the midpoint of line AB is M(2,0),
then the coordinates of B are:
. . A. (-0.5,0.5) . . B. (0.5,0.5) . . C. (-1,0) . . D. (-5,-1)

I don't suppose you made a sketch . . . naw!

      |
      |     A
     1+     o
      |       . 
      |         . M
  - - + - - + - - o - - + -
      |     1     2 .   3
      |               .
    -1+                 ♥
      |                 B
      |

You can see where B must be . . .

 

[Amy12345_1000]

Replying back

Mrspi and Soroban,thank you for helping me out,but unfortunately this question was easy than I though and I solved it to get the correct answer and the teacher checked it too. So apparently I got D.(-5,-1). The easy way to find out if this answer was correct is that: A coordinates are (1,1) and midpoint of line AB is (-2,0). In order to find what the coordinates of B are is by trying to know how we got to (-2,0) of line AB. You have to subtract 3 from A coordinate x which is 1,it will give you -2, and you have to subtract 1 from A coordinate y which is 1,it will give you 0. This will give us the coordinates of line AB.NOW we have to find the coordinates of B is by subtracting 3 and subtract 1 and it will give us (-5,-1). That's how I solved it and got the correct answer. ===================================================================================================================================== Now Mrspi,I was not trying to let people to come and answer the question by doing all the work and I just copy down the answer,because I will not learn a thing from that.I only came here to get some help and apparently it seemed that you were not sure if I came here to let someone do the work for me,or getting some help by telling me the steps on how to solve the problem and letting me do the math and get the answer.I only came here to let someone to explain me on how to solve it and NOT giving me the answers and let them do the work for me.And I forgot to add to say that I want someone to explain each step on what I should do on my first post,my bad.