If the midpoint of A and B is (1,3), what might the end points be?

Question

I'm really having trouble with this one! If anyone could help it would be highly appreciated! :)

I know about finding one endpoint with the midpoint and the other end point but I can't work this out. 

 

Answer 1

To elaborate on Rich's answer, think of the midpoint being the center of a pencil.  Since the pencil could be of any length and any angle, there are an infinite number of answers.  If you want a unique answer, you must pick one of the endpoints, then the other endpoint could be determined.

Answer 2

 

A------------(1,3)------------B

(x,y)                                 (z,w)

 

(x+z)/2=1

x+z=2

x=2-z 

(y+w)/2=3

y+w=6

y=6-w

A=(2-z, 6-w) and B=(z,w), or....

x+z=2

z=2-x

y+w=6

w=6-y

A=(x,y) and B=(2-x, 6-y)

both answers will yield (1,3) as the midpoint for values of x and y or values for z and w

this is all you can do without any more information, along with what the other tutors said

 

Answer 3

It's a pretty open ended question. If the midpoint is (1,3), then it's halfway between the two endpoints. The end points could be:

(0,3) and (2,3) or

(-1,3) and (3,3)

etc.

 

or they could be

 

(1,2) and (1,4) or

(1,1) and (1,5)

 

All of these end points would have a midpoint of (1,3)