The midpoint of a line segment of AB is (4,7). What are possible coordinates?

Question

The midpoint of a line segment of AB is (4,7). What are some possible coordinates for A and B?

Answer 1

A and B could be endpoints of thediameter of a circle of radius r and center (4,7), where 2r is the length of AB.

(x-4)² + (y-7)² = r²

Answer 2

There are infinite answers to this depending upon the length of the line

and the slope

 

We have midpoint = (4, 7)

 

The simplest possible points to look at would be a given distance

straight up and down or straight left and right from (4,7)

 

Perhaps the endpoints are n unit up and down:  (4,7-n), (4,7+n)

Perhaps the endpoints are n units right and left:  (4-n, 7), (4+n, 7)

Pick any number for n

Example: n=1 ... A = (4,6), B= (4,8)    vertical line segment

                         A = (3,7), B = (5,7)   horizontal line segment

 

If the line is not vertical or horizontal, we could pick a slope and then

use the point slope form to find the equation of the line... and then

look for points on the line equidistant from (4, 7)