153k views
5 votes
AB = 6 and the midpoint of AB has coordinate (2, 3). Give two possible pairs of coordinates for points A and B.

User Indimental
by
5.3k points

1 Answer

3 votes

Let's recall the definition of midpoint coordinates given two ends of a segment of the form: (x1, y1) and (x2 , y2)

xm = x1 + (x2 - x1)/2

ym = y1 + (y2 - y1)/2

so, we have two equations for which we know xm = 2 and ym = 3

2 = x1 + (x2 - x1)/2

3 = y1 + (y2 - y1)/2

So for example if we select that the difference (x2-x1) = 4 then :

2 = x1 + 4/2 = x1 + 2

therefore, x1 = 0

If for the y coordinate, we want to select (y2 - y1) = 2, then:

3 = y1 + 2/2 = y1 +1

y1 = 3 - 1 = 2

Then we can say that a possible option is:

A = (0, 2)

and for B we find x2 and y2 from the equations:

x2 - x1 = 4 then x2 - 0 = 4 then x2 = 4

y2 - y1 = 2 then y2 - 2 = 2 then y2 = 4

which gives B = (4, 4)

User Alvin Stefanus
by
4.8k points