Question

The midpoint of \overline{\text{AB}} AB is M(4, 0)M(4,0). If the coordinates of AA are (3, -1)(3,−1), what are the coordinates of BB?

Answer 1

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. If the coordinates of one endpoint are (x1, y1) and the coordinates of the other endpoint are (x2, y2), then the coordinates of the midpoint are given by:

M = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the coordinates of the midpoint are (4, 0), and the coordinates of AA are (3, -1). Therefore, the coordinates of BB must be (5, 1).

You can confirm this by calculating the midpoint using the coordinates of AA and BB:

M = ((3 + 5)/2, (-1 + 1)/2)

= (4, 0)

This shows that the point (5, 1) is indeed the other endpoint of the line segment, and the coordinates of BB are (5, 1).

Explanation: